I grew up driving crap rear wheel drive cars as a teenager. No traction control, no anti-lock brakes. I haven't had a car rust from the salt in years. Just hose it off at least when salt gets on it. don't be a wuss, get snow tires and drive it.
I didn't spend 35K on a car to not drive it 5 months out of the year here in Michgan.
It's just a Mustang, not a Ferrari for petes sake. Just keep some sick days for the real bad days, stay home and play video games all day!! You are never too old for a snow day.