If you're going to carry a gun for self defense, carry it in a manner you can get to it quickly. Whatever the low probability of that situation, it can happen when you least expect it.

Most of the time the weather is mild enough I can wear a short coat or jacket, making pocket carry a viable solution. Mine is a 3.3" .45, not a mouse gun.

Rather than a belt holster, my cold weather alternative is an Alessi shoulder holster. It's also easier to reach when driving. Much of the time I layer the coat with a down vest, which I can wear inside without attracting attention even if the outer coat comes off. I can conceal a full sized pistol or 3" revolver with ease.

Walking around in cold weather with an open coat may be a give-away that you're armed (or stupid). I don't feel out of place wearing an open coat over a closed vest between the car and a store, however, unless it's really nasty. In any case, I leave my coat open while driving, and outside of the seat belt.