You can ride in the snow. Just make sure there’s enough of it to create a “footing”. Riding in deep snow (not too deep) can be a really good work out for the horse, just bee careful as it can be slippery, have ice underneath it and get stuck in the horses hooves!
The ground can get very hard and bother their hooves. Like Carlie said ice can be dangerous as well. Also, if you don’t have proper shoeing then snow clumps into a ball in your horses hoof and freezes. Here’s a link to a picture since I didn’t describe it well: https://www.wildheartmustangs.com/uploads/5/8/7/1/58711151/9128896_orig.jpg
Hope this answers your question! Stay safe this winter!
It’s fine to ride in the snow just make sure there is no ice for them to slip on and give yourself more time to warm up and cool down because of the closer temperature. I just wouldn’t recommend jumping, galloping or turning really tight because of the lack of traction.