I've used the water refill station inside Cosmic Rays and to me it's the same nasty tasting water that all MK QS serves in their cups of water. MK and epcot QS water tastes bad to me. I didn't know there was one in Odyessy Center, I'll have to try that next time we go to epcot.
HS tastes perfectly fine to me. I've gotten the water at Catalina Eddie's, Rosie's Cafe, and Cargo Bay 7 (they have cups and water coolers out so you can get it yourself) and there was no bad taste so hopefully the refill stations are the same at HS.
The water was chilled.