I try to avoid washing if at all possible during the winter. My two main show horses now are bay and liver chestnut, so even if they are dirty you can't really tell. I tend to wash their socks and maybe their tails and just give them a really good brush down for the rest.
I used to show two greys and with greys it is so hard to hide the dirt. So, I would have to wash and I would either use warm water or if I was at the show when I was washing, I would bring this handy little water heater and you would just stick it in and give it like 15 minutes to heat. I would heat up 3 buckets with 3 sponges, 1 to get them wet (tends to get dirty fast), 1 to put soap in, and one to rinse them off with. Try to make the process go by as fast as possible and have a warm blanket ready for them. Once your done, blanket them and walk them at a good fast walking pace to get them warmed up. Then, I would give them a nice warm mash, which I would heat the water up with my heater.
The heaters are like the coolest things ever. They only cost like $25 dollars and pretty much made my life when I was having to wash greys at horse shows in the cold.