Climate is not such a major consideration when visiting Tibet as many people might imagine, for a place nicknamed the land of snows, theres a surprising lack of snow. The boom in domestic tourism means that Lhasa swells with Chinese tourists in the summer and particularly in the week-long holidays around 1st may and 1st October. Finding accommodation can be trickier during these weeks, so try to have something nailed down by lunch time. Winter is very cold, but some travelers swear by the winter months. There are few travelers about at this time and Lhasa is crowded with drokpas (nomads).
Spring, early summer and late autumn are probably the best times to visit Tibet and th March is a politically sensitive month in the country and there is occasional tightening of restrictions on travelers heading into Tibet at this time, but the weathers pretty good. April brings reliable weather in eastern Tibet and discounts on accommodation and vehicle rental in Lhasa and Mt Everest is particularly clear during April and May.
Trips to Mt Kailash can be undertaken from April to October, although September and October are considered the best months and t October is also the best time to make a trip out to the east the Lhasa and its environs dont get really cold until the end of November.
Its worth trying to time your trip with one of Tibets festivals, the New Year (Losar) in January or February is an excellent time to be in Lhasa, as is the Saga Dawa festival in April or May.