Map from Google - Ukraine

Ukraine has a continental climate with cold winters, and warm summers, which become progressively warmer as you move to the south and east. The southern area, which overlooks the Black Sea, has a slightly milder weather in winter, but we cannot speak of Mediterranean climate (winter is cold anyway) except in the southern coast of the Crimean Peninsula (see Yalta).
Ukraine is a large country, the second largest in Europe, with an area of 603,600 km² (233,050 mi²), is largely occupied by plains (in the east) and hills (in the west).

Winter is freezing in much of Ukraine: the average temperatures are below freezing (0 °C or 32 °F) even during the day, except in the most sheltered areas of Crimea. The average temperature in January is around -3 degrees Celsius (26.5 °F) in the north-west of the country (see Lviv), and decreases gradually as we proceed eastward, being of -5.5 °C (22 °F) in the capital Kiev, and around -6 °C (21 °F) in the eastern areas. Moving south, it a bit, but remains below freezing, around -2/-3 °C (27/28 °F). Snow covers Kiev for a hundred days per year.
Here are the average temperatures of Kiev.
Average temperatures - Kiev
KievJanFebMarAprMayJunJulAugSepOctNovDec
KievJFMAMJJASOND
Min (°C)-9-8-32812131282-2-5
Max (°C)-2-131220222323181130
Min (°F)161827364654555446362823
Max (°F)283037546872737364523732

The coldest periods are those in which the Siberian Anticyclone moves over the country: in these situations, the temperature can drop to -30 °C (-22 °F), and even below. The average winter temperature has increased by a few degrees over the last decades, especially in the inland areas. Anyway, periods of severe cold are still possible, although compared to the past they are less frequent and tend to be shorter.
The coast of the Black Sea is not so mild in winter. In Odessa, the average temperature in January is -1.5 °C (29.5 °F), there are on average 100 days with minimum temperatures below freezing per year, and 40 days with snow, and the cold record of the past 20 years is -23 °C (-9 °F). Here are the average temperatures of Odessa.
Average temperatures - Odessa
OdessaJanFebMarAprMayJunJulAugSepOctNovDec
OdessaJFMAMJJASOND
Min (°C)-4-305101516161161-2
Max (°C)1161219232626211473
Min (°F)252732415059616152433428
Max (°F)343443546673797970574537

The Black Sea, cold in winter, becomes acceptable for swimming in July and August, while it is a bit cool in June and September. In the east, the Sea of Azov, more closed and sheltered, in summer becomes a bit warmer.
Sea temperature - Odessa
OdessaJanFebMarAprMayJunJulAugSepOctNovDec
OdessaJFMAMJJASOND
Sea (°C)7569142022232016129
Sea (°F)454143485768727368615448

The Crimean peninsula and the Sea of Azov are affected by cold winds, sometimes violent. The only area that is relatively mild is the southern part of Crimea (see Yalta), south of the Crimean Mountains: these mountains partially protect the coast from the cold northern wind, and turn it into a down-slope, relatively warm and dry wind. Here the average winter temperatures are about 4/5 °C (39/41 °F).
Average temperatures - Yalta
YaltaJanFebMarAprMayJunJulAugSepOctNovDec
YaltaJFMAMJJASOND
Min (°C)224813172121161174
Max (°C)771014202528282318129
Min (°F)363639465563707061524539
Max (°F)454550576877828273645448

In spring, the temperatures and the sunshine hours grow rapidly. In March, in continental areas the snow melts, which turns into mud and produces can make it difficult to travel on rural roads; in April the first warm days alternate with the return of cold weather, with possible snow and frosts, while in May the temperatures generally start to become permanently pleasant, especially in the second part.

Summer in Ukraine is pleasant in the north-west, with maximum temperatures around 22/23 °C (72/73 °F) in July and August, and it becomes progressively warmer as you move to the east, so that highs are about 23 °C (73 °F) in Kiev and 26 °C (79 °F) in Kharkiv. In the south, summer becomes quite hot, with highs around 26/28 °C (79/82 °F) in the area of the Black Sea: in July the average maximum temperature is 26 °C (79 °F) in Odessa, 28 °C (82 °F) in Yalta, in southern Crimea, and 27/28 °C (81/82 °F) in the south-east inland areas (see Donetsk, Dnipropetrovsk). The minimum temperature increases gradually as well, from the north-west, where it's around 12/13 °C (54/55 °F), to the central areas, where it's around 14/16 °C (57/61 °F), to the shores of the Black Sea, where it goes from 17 °C (63 °F) to 20 °C (68 °F). This means that summer in the Black Sea, especially in Crimea, is similar to that of the northern coast of the Mediterranean (French Riviera, Liguria), although the rains are a bit more frequent, 5/6 days per month.
The inland regions have a lower average temperature than those overlooking the sea, because sometimes they are affected by disturbances of Atlantic origin or by cold air masses from the north, but they are subject to heat waves, which last some days, and can raise the temperature to 33/35 °C (91/95 °F).

In autumn, the temperatures decrease rapidly. September is still a pleasant month in the Black Sea area, with highs around 23 °C (73 °F), while the north it's already cool, with highs around 18 °C (64 °F). Sometimes it can get cold, with the first snowfalls, already in October; however, the turning point occurs in November, when it starts to get cold across the country, and even sunshine becomes scarce.

Kiev

The only mountainous area of some importance in Ucraine is found in the west, south of Lviv, where there is a strip of the Carpathian Mountains, which reaches its highest point in Mount Hoverla, 2,061 metres (6,762 feet) high. Here of course the temperature decreases with altitude, especially in summer, because in winter, cold air often clings to the soil, causing a thermal inversion that keeps the plain cold. In summer, thunderstorms in the mountains are more frequent and abundant.
Other mountains, though less extended, are the aforementioned Crimean Mountains, about 1,500 metres (5,000 feet) high.

Precipitation in Ukraine is quite frequent throughout the year, but not abundant in most of the country, since it hovers between 500 and 600 millimetres (20 and 23.5 inches) per year in the vast interior area occupied by plains and hills. The rainiest season is summer, because of afternoon thunderstorms. Winter, however, is not dry, because precipitation, though not abundant, is quite frequent, and often occurs in the form of light snow.
Here is the average precipitation in Kiev.
Average precipitation - Kiev
KievJanFebMarAprMayJunJulAugSepOctNovDecYear
KievJFMAMJJASONDY
Prec. (mm)454035455565707045455540610
Prec.(in)1.81.61.41.82.22.62.82.81.81.82.21.624
Days1210989101010781012115

In the Black Sea region, precipitation is even more scarce, being below 500 mm (20 in) per year, since the summer thunderstorms occur more rarely. The only area that is quite rainy is the western area of the Carpathians, where precipitation reach 1,200 mm (47 in) per year, in addition to the small area of the Crimean Mountains, where it can reach 1,000 mm (40 in). To the west of the Carpathians there is another flat area, though small, where precipitation exceeds 700 mm (27.5 in) per year.

When to go

The best time to visit Ukraine as a whole runs from mid-May to mid-September. Since in July and August hot days can occur, you can opt for the two periods, mid-May to late June and the first half of September, in order to avoid heat waves, which may occur in midsummer especially the south-central and the east of the country; anyway, those who can stand the heat can go in July and August as well.
For a beach holiday in the Black Sea, the best time is summer (July and August), when you will find a sunny and warm weather, tempered by sea breezes, with a few rainy days.
The sunshine amount in Ukraine is good in summer, especially on the coasts of the Black Sea.

What to pack

In winter: very warm clothes, sweater or fleece, down jacket, fur hat, gloves and scarf. For Jalta: sweater, jacket, raincoat or umbrella.

In summer: in the north-west: spring/autumn clothes, being ready to add or remove the outer layer; umbrella. In the north-east and Kiev: T-shirts and shorts for hot days, jacket and sweater for the evening and cooler days; umbrella.
In the south and the Black Sea: light clothes, a sweatshirt or light jacket for the evening.