When recommending someone avoid rushing into an activity, we still say “Hold your horses.” This is a modern spelling of the idiom. As Wikipedia says
“Hold your hosses” (‘hoss’ being a US slang term for horse) appears in print that way many times from 1843 onwards… The first attested usage in the idiomatic meaning [came] from Picayune (New Orleans) in September 1844, “Oh, hold your hosses, Squire.”
The literal meaning is older:
In Book 23 of the Iliad, Homer writes “Hold your horses!” when referring to Antilochus driving like a maniac in a chariot race.
It seems strange that the idiom has survived the arrival of motorized vehicles, but there is a modern variation: cool your jets, which Stackexchange says originated in the US and was first quoted in a newspaper:
1973 Daily Tribune (Wisconsin Rapids) 29 Jan. 1/1 If you want to cool your jets, just step outside, where it will be about 10 degrees under cloudy skies.