I usually have to wash it in temperatures above 40F. Even if it is above 32F, the wind chill may cause it to actually still be less than 32F, causing icing. I usually use the touchless, with the blower. Typically, you can get away with this in frezing temps, with only the, small left over droplets freezing. A thin coating of lithium grease on your door seals will prevent them from freezing shut. But this will not prevent a larger quantity of water (like from an ice storm) from penetrating and freezing the doors crevaces themselves.
As far as I know, and I have done this for years myself on my other autos, washing with warm water in cold weather does not harm the paint. However, it will strip the wax more quickly so wax coat retention becaomes an issue.