How about one of
these ? I'd worry about it's ability in deep snow though I think you can get (?snow?) tracks for these 6 wheelers too. You wouldn't have to worry about drowning / sinking though getting from the water back onto the ice might be problematical. Plus it would be unique !
If you really think the ice is safe, I'd guess your best bet is a used 4WD pickup or SUV. Bet you can get one cheap now and they have other uses than driving on the frozen lake.