There are two different definitions for riding in the snow.
Riding while it's SNOWING gets your bike wet and can get water into just about everything. I ride through SNOW ON THE GROUND every week if I possibly can. I have one bike with studded tires and motocross type high clearance fenders, just for the snow. The snow on the ground is fine, if you clean your bike after every ride. I don't get slush on really anything because of the fenders. Just the brakes and the fork bridge. I do have fork boots they came with the fork. This bike goes in the snow every winter. It's 10 years old and as good as new. Went for a nice ride yesterday it was about 15 degrees so the snow was nice and fluffy and did not stick to anything. Let your bike cool down before you go in the snow and the snow won't stick as much.
Studded tires are fun on a lake! Nokian 296 tires make glare ice easy. Even frozen footprints or a rough surface is easy if you are carefull.