How cold is too cold to bathe a horse depends upon several factors including whether you have only cold or hot water available, whether you have the appropriate equipment for a cold weather bath, and the overall health of your horse.
A healthy horse should be able to handle a bath with no special treatment into the 50's. Generally, unless we have a show or demo we try not to bath horses in temperatures below the upper 60's. Healthy, cooled out (not overheated from exercise) horses can be bathed into freezing temperatures if you ensure they stay warm throughout the bathing process and until they are completely dry.
For a winter bath, use the hottest water you have access too that is still tolerable for your horse. Hot water cleans better and dries faster. If you only have access to cold water, it's best to work as quickly as you can- preferably with a helper so you can soap and scrape the horse twice as fast. It's important to scrape thoroughly after a bath- preferably with a rubber edged scraper as they will conform to the skin and remove more water.
After you've rinsed thoroughly and scraped well, the procedures are the same for drying out whether you were able to use hot or cold water: Use old towels or any scrap fabric to towel dry as much moisture off the body and legs as you can. Next lay a few old towels across the horse's back, then carefully place a (preferably irish knit) cooler over the horses back and cover with a Personalized Full Body Cooler if possible. DO NO BLANKET at this point. Use only breathable fabrics and use only water absorbing fabrics close to the skin.
Once blanketed, walk your horse around in the warmest area you have access to- an indoor arena, up and down a barn aisle, or even just up and down an windbreak outside. After 10 or 15 minutes, remove the towels under the blankets. The towels should be damp and will expose the dry irish knit to the skin to absorb more. Your horse doesn't need to walk constantly during the drying process, but should not be allowed to become chilled. In very cold temperatures, tie your horse near a hay bag so they can reap the warming benefits of chewing and digestion.
Depending on the thickness of your horses winter coat, drying will take anywhere from 1 hour to several hours. Do not leave your horse unattended until when you ruffle his coat, you can feel that the hair next to the skin is dry.