Of course you can! It is great fun and good for your horse! However, there are several things you have to keep in mind:
* Always be sure about the surface under the snow. It can cover holes and ditches, so I never wander in deep snow on unknown terrain.
* When the snow gets deep for the first time, do the first rides at a walk only, because the horse has to get fit and prepared for trotting and cantering through deep snow - it is rather heavy. But, with enough exercise, your horse will soon be ready to go through even the deepest snow - I sometimes get to ride through chest-deep snow.
* Better not ride when crust has covered the snow - it can injure the legs, especially, at gaits faster than a walk.
* Watch out from spots where snow has covered plain ice. Also, if you will be riding in a smaller area, the tracks you use most often are more likely to become icy and slippery sooner.
Apart from this - enjoy yourself! I don't have an indoor arena either, so I ride in the snow all the time, doing mostly trail rides, some flatwork (dressage), and, if the snow isn't too deep or melting - also some jumping.
I have come a long way, to surrender my shadow to the shadow of my horse.