We use a product callef Orvus livestock soap. Only because sheep can change color from dish soap, so we already have this purchased. But Dawn dish soap works fine on goats.
Are they in with a buck? Mine never feel greasy unless it's breeding season and their hind ends will get "buck funk" on them. Other than that, they stay very clean.
Well, maybe greasy is a bit extreme but just the thought them sleeping in their urine and poo. I clean twice a day but the mornings are horrible! I'll try the dawn dish soap. I heard of someone else using baby wipes?
I would use dish soap or baby shampoo. It may be too cold for that if you are up north though, it's already too cold for that most days down here. I use baby wipes for cleaning udders I would guess it would be ok to use those. You could try a horse curry comb & good brushing followed by a wipe down with baby wipes?
I use the hose and dawn dish soap on really warm days for my 2 goats. It really hasn't been warm enough here lately, but I'll make sure I do it once more before winter actually hits. They like it for the most part. They like getting rubbed all over with soap.