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. But if you only stay in Lhasa, you can go there anytime of the year.
Sun radiation is extremely strong in Tibet. The sunlight in Lhasa is so intense that the city is called Sunlight City. The thin air can neither block off nor retain heat so that the temperature extremes can be met in daytime and the same night respectively in Tibet. However it is not impossible to visit the holy snow land. May, June and September are the tourism season in east Tibet.
Most annual rainfall comes in the rainy season that starts from June to September. Usually it rains at night in Lhasa, Shigatse and Chamdo area. The rainfall may block roads and make travel difficult but the scenery at the time will be the best.
Here is 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. Try to avoid August - landslide could happen in the rainy season.
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.
Ali (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.
Eastern Tibet: 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.
Northern Tibet: 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.