I live in northeast Ohio, and would like to hand wash my car more as well. I could equip and dress myself to deal with the cold (neoprene gloves, warm water, etc.), but water on the driveway would freeze too quickly to allow it to be safe, either while I am washing the car, or afterwards.
I too take my car through a touchless car wash, about once a week or a bit more often. When I get home, there are a few frozen water droplets on the horizontal services. I let them warm in the garage (usually while I'm eating dinner), then go out with a warm, wet microfiber and waterless wash solution and wipe down and then dry.
I don't like how well the wheel wells get done (hardly at all), but I find this process at least lets me keep from losing my mind at how dirty my car is. This weekend, I'll probably do it again but reapply wax as well. Current wax coat has gone through 4 or 5 of these cycles, and is starting to fade.
I do have a question for all you northerners, though. This is the first winter I've gone through since I became serious about correcting and maintaining my paint. It petrifies me to brush snow off my car. I do it as gently as possible, and haven't seen any huge issue, but it can't be good. Do you guys have a tool or technique that is less dangerous than a standard snow brush?