Map from Google - Saudi_Arabia

In Saudi Arabia, the climate is generally desert, and is very hot in summer all over the country; almost everywhere the rains are very scarce and concentrated from November to April. However, there are differences among the various areas to be taken into account.

Saudi Arabia, climate of the coasts
Along both the coasts of western and eastern Saudi Arabia, the climate is desert, and it's particularly mild in winter, even hot in the central and southern part of the Red Sea coast, while in summer it's hot everywhere, but it's sultry on the shores of the Red Sea, while it's a bit drier, and therefore torrid, on the shores of the Persian Gulf.
On the coast of the Red Sea (called Tihamah), the average temperature in January goes from 57 °F in the northernmost part, on the Gulf of Aqaba, where sometimes it can get cold at night, to 77 °F of the southern part, where winter does not exist, and therefore it's hot all year round. Summer is very hot everywhere.
Here are the average temperatures of Al Wajh, in the northern part of the coast.
Average temperatures - Al Wajh
Al WajhJanFebMarAprMayJunJulAugSepOctNovDec
Min (°F)555761687275777775726459
Max (°F)757781869093939591908479

The Red Sea is warm enough for swimming all year round, even in the northern part, although it goes down to 73 °F in February and March, while it gets very warm in summer. In the northernmost part, in the Gulf of Aqaba, it is a bit cool in winter, since it goes down to 70 °F in February and March.
Sea temperature - Al Wajh
Al WajhJanFebMarAprMayJunJulAugSepOctNovDec
Sea (°F)757373757981848684828177

Already in Jeddah, in the central part of the west coast, the average in January is 74.5 °F. Summer is very hot and humid, with highs around 103 °F between June and August, but it's especially the humidity of the sea that makes the heat sweltering. By contrast, in the days when the winds from the interior prevail, the temperature can reach 120 °F. Rainfall is definitely scarce: the rainiest month is November, with just 0.8 inches of rain.
Average temperatures - Jeddah
Min (°F)646466727577798179757268
Max (°F)8484909599100102102100999188

At the latitude of Jeddah, in winter the Red Sea is a bit warmer than the northern part of the coast.
Sea temperature - Jeddah
Sea (°F)797777798284888888868481

Mecca is not right on the coast, however, it lies on the plains and it's still west of the mountains, therefore it's still hot throughout the year, in fact it's even hotter than Jeddah, especially in summer when the maxima stay normally around 108/109 °F. In return, the distance from the sea makes the heat drier, and therefore a bit more bearable. However, Mecca is really a very hot city, since during the day the temperature normally exceeds 105 °F for many months, from May to September; there are about 300 days with more than 86 °F per year, and the daily average of the whole year is even 87 °F. Mecca is therefore one of the hottest big cities in the world.
Average temperatures - Mecca
Min (°F)666670778284848684797368
Max (°F)8890951021081111091091091049590

In Mecca, only 2.9 inches of rain per year fall. Here is the average precipitation.
Average precipitation - Mecca
Prec. (in)

Mecca, Sacred Mosque
Mecca is a very sunny city, but in summer some cloud banks can pass. However, this phenomenon is even more evident in the southern part of the Red Sea coast, which during the summer, from June to September, is affected by the passage of clouds from Africa, due to the southwest monsoon (see below), which on the mountains can also cause some rains. Therefore in Jizan, in July and August there are only 7 hours of sunshine per day, and it is also possible to see some light rain. On the other hand, the high humidity makes the heat sweltering, while the average maximum is still 101 °F in the summer months.
Average temperatures - Jizan
Min (°F)727375798286868684797773
Max (°F)8888919599100100100100999390

On the coast of the Persian Gulf, the climate is sunny and desert. Winter is mild, slightly colder than that of the Red Sea, so it's not warm: the average in January is between 54 and 63 °F; sometimes at night it can get cold, especially in the northern part, near the border with Kuwait, with lows around freezing. Summer is very hot and sunny, a bit less humid than the coast of the Red Sea, because the prevailing wind comes from the northwest, originally from the Iraqi desert, and therefore it does not come directly from the sea.
In Dammam, the average goes from 59 °F in January to 99 °F in July and August. Throughout the year, only 3.5 in of rain fall, concentrated from November to April. During winter, there can be very cool days, or even a little cold at night. Summer is scorchingly hot, with peaks of around 120 °F.
Average temperatures - Dammam
Min (°F)505259687782848477706152
Max (°F)70758493106111113113108998473

The Persian Gulf, in the central part where Dammam is located, is a bit cool from January to March, while it becomes very warm from May to November. In summer, the Persian Gulf becomes the warmest sea in the world, even more than the Red Sea.
Sea temperature - Dammam
Sea (°F)706868738186909191888175

In the northern part, near the border with Kuwait, the sea in winter is a bit colder, so that the temperature drops to 64 °F in February and March. In the southern part, in the small coastal stretch between Qatar and the Emirates, the sea in winter is instead a bit warmer, so much so that it stops at 73 °F.

Saudi Arabia, climate of the Syrian Desert
In the far north, there is an offshoot of the Syrian desert, which has a desert continental climate, with relatively cold winters, also due to the higher altitude, and hot summers. In Turaif, at 2,800 feet above sea level, the average temperature in January is 44.5 °F, and 82.5 °F in July, with highs around 95 °F. During winter, cold waves can occur, in which the temperature can drop to 14 °F, and more rarely (given the low precipitation level) it can even snow. On the contrary, in summer, despite the altitude the temperature can reach 113 °F. Precipitation occurs from October to April and are scarce, around 6 in, while from May to September it never rains.
Average temperatures - Turaif
Min (°F)363745546166707064574637
Max (°F)545764758491959591816857

Saudi Arabia, climate of the plateau
Most of the Arabian Peninsula is occupied by a plateau called Najd, at an altitude ranging between 1,300 and 4,000 feet. In addition to the rocky deserts, there is a series of sandy deserts connected together, called An Nafud, ad-Dahna, and Rub 'al Khali, the latter is the southernmost and largest, a huge expanse of sand. The plateau, desert like almost all of Saudi Arabia, has a fairly uniform climate: almost always sunny, mild in winter with cold nights, very hot in summer, but with low relative humidity. The main differences occur in winter, when the northern part is much colder than the southern.

Rub' al Khali

In Ha'il, located in the north at 3,300 feet above sea level, the average temperature in January is 51 °F, while in July it's 88 °F. In winter the days are usually mild, while nights are often cold. Precipitation amounts to 6 inches per year, with a maximum of 1.6 inches in November, and no rains from June to September.
Average temperatures - Hail
Min (°F)394148596872737570615041
Max (°F)6368758493100102104100907566

The capital Riyadh is located in the center of the country, at 2,000 feet above sea level. Winter, from December to February, is mild: the average in January is 56.5 °F. Sometimes at night the temperature can approach freezing, while there are also hot days, in which the temperature gets close to 85 °F even in winter. Throughout the year, only 4 in of rain fall, from December to May, with a maximum of 1.2 inches per month in March and April. In summer, from June to September, it never rains, and the temperatures are very high, around 111 °F in July and August, but with peaks of 113/117 °F. However, the relative humidity is very low.
Average temperatures - Ryadh
Min (°F)454855647377797973645546
Max (°F)68738291102109111111106978272

Medina is located in the west, at 2,000 feet above sea level like Riyadh, but in winter it's milder than the capital, since it has a January average of 62.5 °F, with highs around 73/77 °F. Sometimes it can get cold at night, but more rarely than in Riyadh, actually in the middle of winter it can often touch 82/86 °F. Summer is similar to that of Riyadh, very hot and sunny.
In the south, the desert of Rub 'al Khali, uninhabited and mysterious, is quite warm even in winter, with highs around 77/79 °F even in January. At night it can get pretty cool, but it does not drop below freezing. In summer, the southernmost part of this desert is touched by the south-west monsoon, so that some cloud banks may pass, and sometimes even a downpour may occur.
In Saudi Arabia, there are practically no rivers of any importance, but as happens in desert countries, there are many dry riverbeds, called wadis, which can sometimes turn into ephemeral streams after heavy showers, which are usually short but can be violent.

Saudi Arabia, climate of the western mountains
The western part of Saudi Arabia, known as Hejaz, is crossed by a mountain range parallel to the coast of the Red Sea. In the north (the area circled in green) the climate is desert, with no summer rainfall, though some rains are possible in winter, and even snow at the highest altitudes, as happens in Jebel al Lawz, 8,465 feet high, in the north-west.
In the southern part of the mountainous, in the region of Asir (burgundy area), there are several peaks above 6,500 feet, among which is the highest mountain of Saudi Arabia, Jabal Sawda, 9,843 feet high. Here, the climate is obviously tempered by the altitude, and besides in summer, especially in the southern part, is influenced by the southwest monsoon, a wet south-western current affecting southern Arabia, which brings a bit of rain from June to September, as well as widespread cloudiness. Even in spring, between March and May, some rain may fall. In some areas, precipitation exceeds even 10 inches per year, so the climate becomes semi-arid; on the south-west facing slopes, there are verdant landscapes and terraces in which water springs are used for irrigation.
In Abha, at 6,500 feet above sea level, the average temperature in January is 56.5 °F, that of July is 75 °F.
Average temperatures - Abha
Min (°F)464852555963636359524845
Max (°F)687073778288888684797370

Here is the average precipitation in Abha.
Average precipitation - Abha
Prec. (in)0.30.521.

Asir Mountains, Arabia

When to go

In most of Saudi Arabia, where the winter is mild (northern Red Sea coast, central plateau where Riyadh and Medina are located, Persian Gulf coast) and in the warmer areas (Mecca, Jeddah, south-central Red Sea coast and Rub 'al Khali), the best time is from December to February, to avoid the heat that can be scorching in the rest of the year (but especially in summer).
However, in the northern areas, north of Riyadh (see Ha'il, Rafha, Tabuk) you can avoid winter, which can be cold, choosing the months of March and November. In the far north, in the Syrian desert (see Turayf, Al Qurayyat) where the winter is longer, you can choose April and October.
For a stay at the sea, the best month is November in the Persian Gulf (in March the sea is still a bit cool, while in April it starts to get hot), and March and November in the north-central part of the Red Sea, while you can go from November to March in the south-central part of the Red Sea, from Jeddah down to the border with Yemen, because in these parts the sea is warm even in winter.
In summer, it's too hot for sunbathing.

What to pack

In winter: in the Syrian desert, warm clothes, down jacket, hat, raincoat or umbrella, scarf. In the Persian Gulf coast, spring/autumn clothes, t-shirt or shirt for warm days, sweater and jacket for the south central part (see Dammam, Al Khobar), heavier jacket and hat for the northern part (Khafji), scarf for the wind, possibly an umbrella. For the Red Sea coast, north of Jeddah, light clothes for the day, sweater and light jacket for the evening, which sometimes can also be used in Jeddah and Mecca; in the southern part (see Jizan), simply a scarf for the breeze and possibly a light sweatshirt for the evening. For the plateau, Riyadh and Medina, spring/autumn clothes, warm jacket and hat for the evening especially in the north; for the Rub 'al Khali, light clothes for the day, scarf or turban, desert boots or sandals, sweater or jacket for the evening and early morning. For the western mountains, in the north, warm clothes, down jacket and sweater; in the south, spring/autumn clothes, light for the day, sun hat, sweater and jacket for the evening.

In summer: for the Syrian desert and the plateau above 2,300 feet (see Ha'il), light clothes, sun hat, sweatshirt or sweater for the evening, scarf; for Mecca, the plateau and Riyadh, the Rub 'al Khali and the coasts of the Persian Gulf and the Red Sea, lightweight clothes, long and made of natural fabric (cotton or linen), desert turban, sweatshirt and scarf for air conditioned places. For the western mountains, light clothes for the day, sun hat or desert turban, sweatshirt or sweater for the evening, hiking shoes; for the southern part, raincoat or umbrella.

Women should cover their entire body.