If there's clean water available -- or
any water available, really, even if it's dirty -- they won't let themselves get dehydrated. They may ration themselves on it if they're weirded out or if it's maybe not the cleanest water or whatever, and molasses or kool-aid or gatorade or something to entice them to drink certainly won't hurt....but any goat in its right mind would drink whatever's available before becoming truly dehydrated.
Generally speaking, goats don't use much water anyway.. We carry a few gallons down to the barn at night and across 10 head, they'll drink
maybe 2gal after they finish their grain and start in on the fresh hay. We fill it back up to the top and leave, and the next evening, it's usually still full from the night before. They also have a stock tank with a de-icer in the barnyard, but it's rare to see any of the goats drinking out of it. It was scrubbed and sanitized after the weather dropped off too cold for algae and all that good stuff to have come back, so it's crystal clear water...they just don't use it.
If it would help to make you feel any better, it's pretty easy to check a goat for dehydration. Just like parasitic anemia, dehydration shows up in the eyelids first. All ya gotta do is pinch their upper eyelid between your thumb and forefinger and then let it go... If it snaps back, they're fine; if it's stays tented up for a bit, they're dehydrated.