@simrin-- Yea, I guess it might be difficult for people to understand if they haven't been around horses. I live on a farm with many horses, so I completely understand what this expression means. It's so straightforward and logical when you know about how horses are taken care of.
We ride our horses on the weekends usually and they really do sweat when they run a lot. What we do is we let them hang out and walk around the stable to cool down. We also have towels for them and we literally absorb the sweat off their bodies so that they don't get cold. It's sort of like when a child sweats after playing and you have to change his shirt to make sure he doesn't get the chills.
Once my brother put our one horse in the stable without doing this and she was ill for a whole week after that. The veterinarian had to give her antibiotics.