I drove my '28 Special Coupe for a whole year when I first got it, just to do it and say I could.
It started easily the coldest day of that year (-2*F), and ran reliably. Traction was another story, as I have stock 4.50x21 tires, and an agressive tread is not available, nor do I have chains...
The down side is exposure to corrosive road treatments; if they salt or brine the roads in your area, leave the A in the garage and wait until spring rains have washed all traces away... even salt dust from dry winter roads will get into the nooks and crannies, and when the car gets wet, the salt will go to work.
Because Pennsylvania loves to go crazy with the salt, I put my A away when the first snow flies. I saw the salt damage from one season, and won't subject it to another.
Rain is another story... make sure your top is water-tight, so that your interior doesn't get water-stained.
SC Frank