Yes you can. I am in 4-h and I have to give mine bathes all the time at fair. you have o use a soap like dish soap...
Can I give a goat a bath - Page 2
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If you want to get "pet" goats. Get wethers. They are the easiest to tame and least moody. They do not have the offensive habits of their non castrated male counterparts. Our Toggenburgs like water and can be bathed without issue.
Wethers make great pack animals, too. I have 3 I'm raising for that purpose. They carry camping gear into the mountains for us. Next year they will be carrying 40 lb each. They've had to be taught to tolerate getting wet. And they poop and pee whenever, and wherever, they want. But they troop right along with us wherever we go, thru the water, up and down the mountains. They're intelligent, good natured, and a lot of fun!