Goats do not have sweat glands like horses do.
I do not think it is an expense you should need for your goats. With proper management, they should not need coats. That being said, I have a 12 year old pet goat that will likely get a coat this year. She's a very tough old lady and she hardly seems like 12 years old, but that may be due to the fact she's my first goat and gets some special treatment, lol.
One interesting thing about coats on goats is that they itch on fences and then sometimes get clipped to the fence by the clips on the coat. We had an animal with a wound that she wouldn't leave alone, so we put a coat on her to keep her away from it. We ended up replacing all of the plastic snaps on the coat with those oval things that you screw shut, so she wouldn't get stuck anymore.