First I'd take a bucket of warm water and dip her tail in it to get it wet and rinse out some of the nastiness. Then I'd lather up the tail and rinse it in the warm water. With my horses I can take the bucket right up to the dock of their tail with the tail in it to get the most of the tail wet & rinsed. After rinsing out the soap and most of the yuck, I'd take some kind of oil, olive oil, corn oil etc, to put on the pitchy parts and work that through to dissolve it. Then I'd was the oil out and put a nice leave in conditioner on the tail. As long as it's just the tail getting wet, the horse shouldn't get cold. I'd take old towelling and squeeze the excess water out of the tail, so it wouldn't drip on the horses legs.