Oberammergau is a year-round Alpine village. The decisive question is whether or not you are visiting in a Passion Play year — they fall every decade ending in zero. In a play year the village sees roughly 450,000 visitors between May and October; rooms book out a year ahead and prices double. Outside those years the place is calm.
Summer (June–September) is the peak season for walking, cable cars, and beer gardens. Temperatures sit in the low 20s with cool nights — pleasant for Alpine hikes. Winter (December–March) brings reliable snow at the cable-car height and quiet skiing at Kolbensattel; the village is at its prettiest under a fresh fall. Spring and autumn are the off-season — lifts may be closed for maintenance and some restaurants take long holidays, but you have the painted streets largely to yourself and room rates fall sharply.