While I don't really know, I have my doubts that the "wash & wax" soaps will do much for you.
Options?
1. Use one of the rinseless wash product that seem to leave at least something behind. I have no idea how much if any they will protect.
2. Use a spray wax that wipes on and off like a QD.
Poorboy's Quick Wax+
Optimum Car Wax
Duragloss Aqua Wax
Mothers makes at least two
I know there's many others as well.
You could check with the suppliers and see at what low temperature point they won't work.
3. Find a friend or relative that would let you use their enclosed space once or twice a year. A hand wax won't take a lot of time or space.
You don't list your location, but even in Iowa, we get a day or two of warmer weather a few times during the winter. Even without heat, my garage is usually about 10 degrees warmer than outside. 40/50 degree day, 50/60 degree garage. Not the best, but it can be made to work.