I would suggest trying to find a triple jogging stroller, and you would have no problem in the snow. I LOVE my double jogging stroller, and use that if we have to go in the snow. IF not, I tie those plastic sleds (for ages up to 2/3, $14 @ Canadian Tire) together, and have a train!
I have used the wagon in the snow but only if there's little to no snow on the ground.
Up until recently, I have used my stroller, and tied the wagon to it to walk around - now I have my Choo Choo Wagon (not to be used in the winter).