I stayed at Mammoth campground during a winter visit of Yellowstone mid March of this year. his is the only campground open in Yellowstone during the winter season.  Mammoth is a first-come, first-serve campground with a cost is$20 a night, cost is the same during the summer season. The campground can still fill up on the weekends, this is because only the first loop is open during the winter season cutting your campsite availability down quite a bit. The campground has paved roads with gravel parking pads. Sites have platforms for the tents. Dumpsters and recycling is available at the entrance. The campground has only one restroom open in the winter at the entrance. Each site has its own bear proof food locker, as well as a picnic table and metal fire ring. While the campground and Mammoth area had little snow on my March visit you could still be camping on snow easily in March, as heavy snows can happen at any time.  Visited the area 6 weeks later and it had much more snow, so be prepared to camp in snow as late at May.