When I moved my horse into my last boarding-barn situation, I took him out the same day and went on a group trail ride. It wasn't really planned - I just went to check on him and was invited to join a group that was going out for a short evening ride.
Unless it involves a long haul to get to our destination, there's no reason why I wouldn't take my horse out the day of arrival for just a bit of exercise. When we haul 6+ hours for a camping trip, though, we usually give them the rest of the day to just "chill" and start riding the following day.
It also helps to know your horse, and how it responds to the change.
"Parelli horsemanship is just like painting by the numbers. You need absolutely no skill. You just put this color here and this color there, and when you're done, you have ... a mess no one wants." mp