So after noodling on different options we finally came up with a solution - a mixing bowl that drains into a small, portable gray water container and a soap/lotion pump for the water source. We have our Cabela's camp kitchen for dishes, so this literally is just for brushing teeth and rinsing my fingers before handling my contacts...so a tiny amount of water is perfect. I'd say the pump container holds about 16-18 oz. And if we need to refill it every day, so be it...but during our prototype trial in the bathroom at home we were all three able to brush our teeth for two nights with the amount in the full bottle.
Viola! No winterizing or anything to mess with, but the convenience of a little spit sink!