It depends on age and event and how tired they are
It depends on how many days the competion was and also how long the journey was, for example, I went to compete on a three day competion, that was a three day journey for my mare to get there, when she came back, I gave her 1 week to rest, only walking her! But if it is a close competion I usually give one day!
I guess it depends on the amount they did but I usually give mine one or two days off after a 2-3 day competition just because I can. Or one day off then a light walk or hack to the beach or something