A number of explanations, all unverified, have been offered for the origins of the phrase, dating back to usage in Ancient Greece.
"Cool your jets" is an essentially identical idiom.
Someone is to slow down when going too fast,[1] or to wait a moment, or to be more careful,[2] or to be patient before acting.
[3] For example, "Hold your horses, we have not won yet, so don't start celebrating.
"[2] There are several sources documenting the usage of "hold your horses"