Yep feel free to wash em at will
Just remember water is like acid to goats so you might be in for a fight! But if you do it enough they get used to it pretty fast. Legion, my pack goat has had water training since he was just a few months old and now not only follows me into the water when I go fishing but actually prefers it on hot days. Instead of eating at the bank, he will stands out in the water with me waiting for me to catch a fish.