A RWD car, like the Mustang, definitely needs winter tires if it is going to transport you in safety during the winter season.
In my neighborhood, one of the residents apparently does not learn from experience. A few years ago, while everyone else was getting around okay (albeit slowly) in a moderate snowfall, this guy got stuck while trying to make a turn from the county road onto his own street. The Mustang got bogged down in what was probably no more than 4 inches of snow, and he had to get a tow truck to pull him onto a straight section of the road.
Well, fast forward to the following winter. Again, a moderate snowfall was causing everyone to drive with caution, even though the roads were passable. Guess what? As I passed the Mustang owner’s street, there he was–hung up in just a few inches of snow in the exact same place where he got stuck during the previous winter!
While it is possible that this guy’s driving style is also a factor in his getting stuck, it is also reality that a RWD vehicle is going to have problems in the snow–especially if it is shod with high performance “summer tires”.
Get yourself a set of 4 winter tires (I recommend the Michelin X-Ice tires) mounted on their own set of steel wheels. That way, you can do the seasonal change-over whenever you want, and at no extra cost for each change-over.