Book a chalet or apartement
Most rentals are cheaper than hotels. You either go out for dinner, or cook your own meals. There are restaurants and grocery stores in Zermatt, so that's no problem whatsoever.
Find a chalet or apartment in Zermatt. The best price is guaranteed. Please see the e-domizil website:
www.e-domizil.ch/holiday-houses/ch/zermatt/zermatt/1475/1044126/