Use or find a cheap trolling motor. I suppose you've got electric there, anyway. Get an inverter and plug it in. I've done this before to keep an open hole for waterfowl. We didn't, and you may not, have the luxury of electricity. If you're kinda handy, you can just disconnect the head and extend your wiring. This way you can put the prop faceing towards the ground, pulling the warmer water off of the bottom.
I'd say we have similiar winters. Keeping the motor running at night is the key. Wind and sunshine keeps a lot of holes open, or at least open enough to kick on the motor just before dark, again.