Map from Google - Oman

In Oman, the climate is tropical desert almost everywhere, with some summer rains in both the northern and southern mountain areas, and clouds brought by the summer monsoon along the eastern coast. The monsoon, from mid-June to mid-September, is due to wet currents blowing towards the Asian continent, and brings limited effects in terms of rain, but it's nonetheless able to influence the climate of the country.
The map below shows the climate zones of Oman.
Climates in Oman
Along the coast of the Gulf of Oman (zone 1 in the map) the climate is desert and sunny all year-round, with a few winter rains, more likely in the far north, ie the Musandam Peninsula, an exclave of Oman in the United Arab Emirates, where 0.6/0.8 inches of rain per month fall from December to March. This area is very hot in summer, with highs around 99/100 °F on average, and the humidity of the sea that makes the heat oppressive. When the wind blows from inland the humidity drops, but the temperature can approach 120 °F. The winter temperature is pleasant: the daily average is around 68 °F in the far north, and 70 °F in Muscat, the capital. In contrast to the northern tip, in summer, along the northern coast (called Al Batinah) where Muscat is located, the hottest month is June, because in July and August the clouds brought by the southwest monsoon can lower a bit the daytime temperature, which passes from 104 °F in June to 100 °F in July and 96 °F in August.
Here are the average temperatures of Muscat.
Average temperatures - Muscat
MuscatJanFebMarAprMayJunJulAugSepOctNovDec
MuscatJFMAMJJASOND
Min (°F)636468758486868281757064
Max (°F)777986951041041009797958681

In Muscat the rains are very scarce, given that they amount to 4 inches per year, and in summer the rains are virtually nonexistent. Here is the average precipitation.
Average precipitation - Muscat
MuscatJanFebMarAprMayJunJulAugSepOctNovDecYear
MuscatJFMAMJJASONDY
Prec. (in)0.91.10.60.40.200.10.2000.20.44.1
Days23210111000213

The Gulf of Oman is warm enough for swimming all year round, and it gets very warm in summer, as we can see in the following table.
Sea temperature - Muscat
MuscatJanFebMarAprMayJunJulAugSepOctNovDec
MuscatJFMAMJJASOND
Sea (°F)757575818488888684848177

Muscat

In the Musandam Peninsula, there are mountains which reach their highest point in Jebel Al Harim, 6,847 feet high, but they are desert, because in summer they do not receive rainfall.
In the mountains located south of the northern coast (zone 2 on the map), called Al Hajar, and culminating in Jebel Shams, 9,872 feet high, the south-west monsoon brings a bit of rain, which added to the modest rains (and sometimes even snowfalls) of winter, raises the total of the year in some areas above 8/12 inches, still not much, but sufficient for the growth of some shrubs or drought-resistant plants. In Saiq, at almost 6,500 feet above sea level, the average temperature in January is 50 °F, so it is quite low, with possible frosts at night. In June and July, highs are around 84/86 °F. On the contrary, at lower altitude the summer heat is scorching.
Average temperatures - Saiq
SaiqJanFebMarAprMayJunJulAugSepOctNovDec
SaiqJFMAMJJASOND
Min (°F)414550576468706863554843
Max (°F)596468758488888682756863

In Saiq, 12 inches of rain per year fall, with a relative maximum in summer. Here is the average precipitation.
Average precipitation - Saiq
SaiqJanFebMarAprMayJunJulAugSepOctNovDecYear
SaiqJFMAMJJASONDY
Prec. (in)0.81.21.41.20.80.61.821.20.60.40.412.2
Days23322344211127

Along the coast of the Arabian Sea (zone 3) the climate is desert; moving south, winter gets progressively warmer, while summer becomes less hot, but also more humid and cloudy, due to the greater influence of south-west monsoon. A moderate wind blows often, making the sea choppy. However, there can be periods that typically last two or three days, in which the wind blows from inland, causing sudden increases in temperature, especially from April to July, with peaks above 105 °F, often accompanied by sandstorms; these events are more likely in the northern part of the coast, while in the south the coast of Dhofar is more sheltered from these hot winds.
In the island of Masirah, the temperature is high even in winter; in this season there is little rain and the sun shines. The temperature gradually increases in April, May and June, when it reaches 95 °F, then it moves back to 87/89 °F in July and August, when humidity and cloudiness increase, even though the rains are still scarce. Here, just 1.6 inches of rain per year fall.
Average temperatures - Masirah
MasirahJanFebMarAprMayJunJulAugSepOctNovDec
MasirahJFMAMJJASOND
Min (°F)666670757979757375737370
Max (°F)818286939795908888908682

The effects of the monsoon are more evident in the southern part of the coast. In Salalah, the capital of Dhofar, the daytime temperature reaches 90/91 °F in May and June, but then it goes down to 81/83 °F in July and August, when even a bit of rain falls, just 0.8/1 inches per month, under the form of frequent drizzle. In addition, in July and August a permanent cloud cover is formed on this part of the coast; for this reason the daily temperature range is narrow.
Average temperatures - Salalah
SalalahJanFebMarAprMayJunJulAugSepOctNovDec
SalalahJFMAMJJASOND
Min (°F)666872758181777575737268
Max (°F)828286909190848184888884

Here is the average precipitation in Salalah. Although in July and August there are "officially" only 7/8 days of rain per month, days with light drizzle occur more often.
Average precipitation - Salalah
SalalahJanFebMarAprMayJunJulAugSepOctNovDecYear
SalalahJFMAMJJASONDY
Prec. (in)000.20.20.30.30.910.40.200.23.8
Days02011378300025

The Arabian Sea is warm enough for swimming all year round, and it is warmer in spring and autumn, while in summer the water temperature drops a bit, because the wind increases evaporation and mixes the water layers.
Sea temperature - Salalah
SalalahJanFebMarAprMayJunJulAugSepOctNovDec
SalalahJFMAMJJASOND
Sea (°F)777779828482777577828179

In the southern coastal range (zone 4) of the Dhofar region, north of Salalah, the climate is cooled by the altitude, and the summer monsoon succeeds in discharging a bit of rain, so that the landscape is green, at least along the southern slopes exposed and during the rainy season. At 2,300/3,300 feet above sea level, the temperatures are mild in winter, around 70/72 °F during the day, and similar in summer, while in spring and autumn they are higher, around 82/86 °F. In summer, the rains are usually light but they occur almost daily.
Here are the average temperatures of Qairoon Hairitti, at 2,800 feet above sea level.
Average temperatures - Qairoon
QairoonJanFebMarAprMayJunJulAugSepOctNovDec
QairoonJFMAMJJASOND
Min (°F)555763687070686666666357
Max (°F)707377848684737079827972

Dhofar mountains

In the vast inland desert area (zone 5) which covers most of the country, the climate is desert, mild in winter (with cool nights and warm days), and hot in summer, with average highs regularly above 105 °F, but with peaks of around 120 °F. Even here, however, in summer some cloud banks can pass, and there's a slight decrease in maximum temperatures in July and August, but generally it doesn't rain.
Average temperatures - Haima
HaimaJanFebMarAprMayJunJulAugSepOctNovDec
HaimaJFMAMJJASOND
Min (°F)545763727781827775706459
Max (°F)818691102109111108108104999184

Every now and then, from May to November, Oman can be reached by tropical cyclones, which bring gale force winds and torrential rainfall, as happened with cyclone Keila on early November 2011.

When to go

The best time to visit Oman, making excursions in the desert, in cities and in mountains, is winter, from December to February, which is sunny, pleasantly warm on the coast, and quite warm in the desert, during the day (but cool at night), and sometimes cold in the mountains.
For a beach vacation, as we have seen the sea is warm all year round; the sea temperature is good even in the period from November to March, but in November there is still some risk of cyclones on the coast of the Arabian Sea, while in January the temperature can sometimes be a bit cool in the coast of the Gulf of Oman, at least for those who are sensitive to cold.

What to pack

In winter: in Muscat and the north, light clothes for the day, sweater and jacket for the evening and cool days, scarf for the wind. For the high mountains, spring/autumn clothes, sweater and jacket for the evening. For the desert, light clothes for the day, scarf or turban, desert boots or sandals, sweater or jacket for the evening and early morning. For the Arabian Sea coast (see Salalah and Masirah), light clothing, a sweatshirt for the evening. For the southern coastal range, light clothes for the day, sweater and jacket for the evening. For the reef, snorkeling equipment, water shoes or rubber soled shoes.

In summer: in Muscat, the north and the desert, loose fitting, lightweight clothes, made of natural fabric (cotton or linen), desert turban, sweater and scarf for air conditioned places. For the high mountains, light clothes, sun hat, a sweatshirt for the evening. For the Arabian Sea coast (see Salalah and Masirah), light clothes, light sweatshirt and scarf for the breeze, light raincoat. For the southern coastal range, spring/autumn clothes, a light jacket and a sweatshirt, raincoat.
For women, it is better to avoid shorts and miniskirts outside tourist resorts.