Bah! Don't sell the stang! Just get a set of Dunlop M3's and your stang will be as capable in the snow as 99% of the trucks and suvs that are out there. Even though I have a relatively wide set of 245/45/17 they perform incredibly. Before I got the tires I would have trouble getting out of my parking lot with just an inch or two on the ground. In order to test the limits of their traction I did everything I could to try and get stuck. I was unable to create a situation where I couldn't go where I wanted to. Even on steep snow covered inclines where others were having trouble I could come from a dead stop and pull away with confidence.
As far as weight goes I put a hundred pounds of salt in my trunk once and the only thing it seemed to do was warp the floor of the trunk. And it is absolutely not needed with a good set of tires.
Anyway I really can't say enough of the importance of having a good set of snow tires for a DD stang. They've certainly made driving in winter a lot of fun.