The ski season runs from early December to late April, with the best snow usually between mid-January and early March. The south-facing exposure that gives Alpe d'Huez its "island in the sun" branding is a double-edged thing: glorious blue-sky skiing days, but snow on the lower slopes turns to slush quickly in spring.
Summer is the other proper season, with the lifts open from late June to early September for hikers and mountain bikers. The Tour de France often visits in July, which is spectacular if you can get yourself in position but a mess for traffic and accommodation. The shoulder months — May, October, November — see most of the resort closed.