Snow doesn’t have to be the end of your ability to ride. If you know the footing under the snow and ice isn’t and issue then it can be fun to ride.
I grew up in Maine and I remember riding when the snow was belly deep on my pony. My mom would often break the trail with her horse first. Our favorite place to ride was in a big field where we knew the footing. The snow was untouched and we would make paths and play games.
This is a video of a recent ride that we took in the snow. We were in New Mexico and the footing under the snow was sandy. We also had a guide that knew the trails well.