I ride all winter but our barn has an indoor arena so that makes things easier!
Still, we've ridden outside and on trail in the winter, here are the tips I use:
1. If it's below 25 degrees F I don't bother, too cold for both of us, not good on either of our lungs, esp outside!
2. Bareback is nice and warm so I love that every now and then, and get a good pair of insulated boots so your tootsies don't freeze!
3. You can get a quarter sheet for your horse if you're worried about him getting cold, they'll keep him cosy and go right underneath the saddle pad and saddle.
4. My girl is barefoot so she never has the snowballs under the hooves issue, but for my friends with shod ponies, you can use Pam cooking spray to help deter the snowballs!
5. When outside, I go slower! Esp. in deep snow...if you ask your horse to run around in deep snow you're inviting some potential accidents with slipping on icy/snowy areas and/or bowing tendons (much like in deep mud). Also if the snow has a sort of icy crust on top that the legs would break through they could potentially get cut if it's sharp enough.
6. Because my girl is ridden and in training all year round, I use a trace clip on her once she grows in her fuzzy winter coat, so that I can get around the sweating issue - because the LAST thing you want to do is put your horse's blanket back on with him being sweaty! The first year I got my girl I didn't know about the trace clip so I left her fuzzy and BOY was she a FUZZBALL! She got so sweaty that I had to use a hair dryer to dry her off after our rides before I could put her blanket back on! Not that she minded the warm air on her, but it took a good long time!