Since we're assuming a unit of trained bear cavalry and not some drunken rednecks-in-tin-cans that said, "Hold my ale..." and tried to go all "8 seconds" on wild bears, and also that these troops are headquartered (and possibly trained at this place), there's probably been generations of war-bears raised and trained as battle mounts...
Hell, one dwarf could have raised and ridden eight generations of bears from the same line into battle.
You could go full Game of Thrones and have these guys be part of an organization like the Night's Watch, an Order of Rangers riding around the mountains keeping the orcs at bay and protecting travelers... If they're operating out of Deadsnow, you should probably have a small keep and stable beside it for the Order of Bear Riders and have the monastery operating a side hustle catering to the needs of the local travelers since they're dedicated to the God of Wanderers.
As for the bears' stats, you might want to look at the sidekick rules as mentioned for things like giving them decent AC and HP, etc. Maybe they have a small suite of actions they're trained to take on their own if not being ridden or otherwise commanded by their rider - attack the same target as their rider, use a help action, drag their unconscious rider out of the fight, etc....
Some adventure ideas...
- Maybe there's an ancient magical pact between the bears and their riders - there's an ancient noble line of bears (smarter than your average bear, lol) that has willingly sworn themselves to the same cause as the dwarves that ride them...
Something could threaten that pact:
- maybe the orc hordes have taken possession of some magical whichamawhatsit related to the pact and the party needs to get it back before the orcs (and whoever is helping them) can destroy it and bring about the downfall of the Order.
- maybe the orcs have seized control of the bears' ancient hidden breeding grounds, or the "long-lost" citadel where the order was founded...
- maybe the half-dozen party members are the last of the far-fallen Order, and need to reach one of the above places or achieve some other goal in order to begin rebuilding the Order or otherwise restore it to glory...