In fact, the Tibetan climate is not as harsh as many people imagine it to be. It is suitable for travel to Tibet from April to the beginning of November, and the best time is August and September. Sun radiation is extremely strong in Tibet. The sunlight in Lhasa is so intense that the city is called Sun City.
The thin air can neither block off nor retain heat so that the temperature extremes can be met in daytime as well as night. Most annual rainfall comes in the rainy season that starts from June to September, however, it's relatively drier than other Himalayan countries as much of the monsoon clouds from the south are blocked by the high Himalaya. If you are traveling overland to Nepal, the road conditions towards the border and in Nepal side can be in bad condition during the rainy season.
Here are some more specific information in different areas:
Lhasa - Shigatse - Lhatse - Tingri - Nyalan
Along the Friendship highway is basically in good conditions year around. But from December to February, the thawed road could make some trouble.
Mt. Everest Area
Early May and early October are the best time to visit Mt. Everest. Due to the clear weather, you have great chance to see Mt. Everest's true face (if you are lucky). From December to February, you'd better not to go to this area because it is too cold - except you are real Great Adventure People.
West Tibet and Mt.Kailash
Even without climate restrictions, this area is already inhospitable. Big rain and snow could make the journey worse. However, for those determined tourists, the appropriate time is May, June, July, September and October.
Don't go to this area in July or August (the rainy season) because the rain could ruin the road, and make terrible landslides. In winter, the road could be frozen.
With the average altitude of 4,500m, this area offers very limited time for tourists. Summer (July to August) is the prime time to enjoy the great plain in northern Tibet.