Depending on the type of mud, it can completely coat the tire until it's no more than a slick covered with clay type mud. Then you can spin those tires until the cows come home.
While not as handy as a true winch, they do work. We used to make our own. We'd take an adapter for converting single wheels to dual wheels and then just attach a rim to that. You could put it on any of the drive wheels (assuming 4 wheel drive) that was accessable. Took less than five minutes to put on the "winch" and then what ever your rigging time was. Until I got an electric winch this was in my box of tricks. Actually it stayed for quite a while after. It's still in the garage, I think up on the rafters.