My advice would be to put a tarp or cover over the front of the bike to maybe keep some of it from freezing too much overnight. Also put some WD-40 (or the like) inside the throttle grip area, just to make sure moisture doesn't stay on the grip. WD-40 displaces moisture, therefore it might make it less likely to freeze up. Although, since I live in Texas, I don't know what 5 degree weather does to mopeds, so you might have to improvise a bit.
Hope this helps,