Ouch, cold showers in cold air. You are a real he-man to try.
That solar thing is a waste if the sun isn't shining (had one) and with cold air circulating around it you might just lose the warmth of the bit of sun you get. I suppose you cold fill it with water that you heat on the stove but still it is going to be difficult. Keeping warm sounds like a serious problem in 60 deg or less. If it is only for the weekend you could use baby wipes to get semi clean. They do have a bit of scent to them for an added feature.