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 extreme 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 the 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 on the Nepal side can be harmful 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 condition year-round. But from December to February, the thawed road could cause 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 a great chance to see Mt. Everest's real 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. Significant 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 possibly frozen.
With the average altitude of 4,500m, this area offers minimal time for tourists. Summer (July to August) is the prime time to enjoy the vast plain in northern Tibet.