Deer actually get fevers when wounded and will seek out water to cool themselves and the wound. Mine did.
ORIGINAL: Rob/PA Bowyer
It's not because it will help them heal up as much as they become thirsty because of lack of blood etc...Also, I've seen them use a creek/water to hide their tracks etc.. a small doe walked a creek, and then back tracked the same creek. It was amazing what she did and we wouldn't have known it other than a fresh snow made it easy.
But yes, many deer will seek water.