Though Zermatt is one of the few Alpine resorts where you can ski year-round (on the Theodul Glacier), there is still an official winter season when the bulk of the lifts, valley runs, and full resort services operate. Outside that main season, glacier lifts may still run, but many of the lower-altitude lifts and runs are closed (or in reduced service). Your best bet is to plan around the core winter window for full access and amenities.
For a full list of coming up events in Zermatt check the page on the tourist office website