I had a cocker spaniel who had really hairy feet / toes. I only trimed them when she slid on tile or wood floors so that her pads were clear but never between the toes.

Yes, trim the feet. I have really feathered feet. The snow will attach to the fur and make walking uncomfortable. Be sure to get the fur from between the pads as well. If your feet get cold, then - hey come inside by the fire and roast marshmellows!