May to September is the most popular season to visit Tibet. The weather is warm with clear skies. The snow/ice starts melting in April clearing the blocked roads and making it easier for you to visit various Tibetan townships. However, since this is the peak season, the prices are at their highest.
If you want to save around 20% of your money you can visit Tibet in either April or between October to November. The weather is cold but there are not a lot of tourists visiting so you get more options for hotels and vehicles.
The lowest tourist season in Tibet is winter (Dec–Feb). The weather is very cold but you have all the attractions to yourself. The hotels and transport are considerably cheaper which means you can get hotels and vehicles in half the price you would pay during the peak tourist season.