This isn't an easy or economical solution but is there any chance that you can run tubing under the snow in the yard? About the only way it might even be feasible is if you could put your tank close to a window and run the in and out from the yard cooler through the window. Still the costs for a larger pump and excess tubing would put the nix to it in my mind unless you're catching and using a ton of bait. Plus, if anything ever gets clogged there could be a mess with the in excess of tank capacity of water flying around.
Alternatively, if you have an old fridge dedicated to either bait, beer or both, you could apply the same concept except route the cooling loop inside the fridge.