It warms them up because it’s HOT butterbeer. Ever drink beer a 180 degrees?
And Ron WANTED to try firewhiskey, but Hermione wouldn’t let him. I don’t recall any underage drinking.
Pretty sure Harry had some in the last book. And I think butterbeer is like hot buttered rum. But that is just my guess on the subject. I think I remember something about someone having too much of it. I forget where.