Will she take a smaller size in the rear and a bigger size in her front?

My 2007 Dodge Magnum (OEM 17" wheels), badly needs Snow tires. I do alot of driving in upstate region of NY and the snow has made it almost impossible on my last trip. This Summer I upgraded to 20" tires and wheels. Can I put a set of 17" steelies on the rear with new Snow Tires and leave the 20" tires/wheels mounted on the front? It will only be for a couple months. I do drive about 150 miles per day. Thanks