Gear up for the thick stuff. Kick , jump , bust up , pound , beat , every inch of cover big enough to hold a bunny.
I had success being the Dog/shooter when I was young. Usually he bunnies will bust out when you are least ready so a 12 gauge with 7s was my choice.
You can still hunt them in the snow with a 22/22mag. Look for those pretty black eyes not far from an area that you think may hold a burrow.
Yesterday the boy and I took both hounds out for an evening hunt. This won't happen to you if you don't have hounds. Both found themselves in leg hold traps and I now have 2 beagles with hopefully only sore feet.
Hounds are great but you can fill the game bag. You will just have to work harder.
Good luck.