The climate in Tibet is not as harsh as many people imagine it to be. It is totally suitable to travel to Tibet from April to the beginning of November and the best time would be August and September. But if it’s only for Lhasa, you can go there any time 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 a 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 it difficult to travel but the scenery at the time can be expected to be at it's best.
Here is some more specific information in different areas:
Lhasa - Shigatse - Lhatse - Tingri - Nyalan:
Along the Friendship highway is basically in a good condition all year around. But from December to February, the thawed road could be 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 appearance (if you are lucky). From December to February, you better not go to this area because it is too cold - except if you are a real great adventurous person.
Ali (Mt. Kailash):
Even without any climate restrictions, this area is already inhospitable. Big rain and snow could make the journey worse. However, for determined tourists, the appropriate times are the months of 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 may have terrible landslides and in winter, the road could be frozen.
With an average altitude of 4,500m, this area offers very limited time for tourists. Summer (July to August) is the best time to visit the great plain in northern Tibet.