I used to wash my car in the winter with small amounts of very warm water and thick rubber gloves. Wash/dry each section at a time. It usually won't freeze if you can do it quick enough. Otherwise, see if you can find an indoor garage with a drain. Once you've got your car relatively clean use a detailing spray every day to get road grime off the car.

Another route would be to use a touchless wash or outdoor wash to get the majority of the grime off the car. Then go with the detailing spray.