It really depends on the tranquilizer and the horse. I have to sedate my horse for shoeing and she gets a half to three quarters of a CC of Dormosedan. I don't ride her at all that day (vet's instructions). I give it IM and I don't know if she's a cheap drunk or what, but it sometimes takes up to 3 hours (after 45-60 min. with the farrier) for her to be fully awake.
However, when she was on stall rest for an injury and finally went back on a riding rehab, my vet had me use a little Ace for the first few rides.
She wasn't running away with me, I just couldn't stop her!
The effects of atravet will last quite a while with most horses, depending on the dose given as well of course. If you give the shot at 3 PM, perhaps 1 or 2 cc IM, I would expect your horse to still be under the influence 3 or 4 hours later if that is when you must ride. Not to the extent that it would be readily apparent to the onlooker, but the horse would still feel the effects. He should be safe to ride by then (not so tranquilized that he is likely to fall down), but still under the effects... less stressed, less reactive, more relaxed than normal. The drug can be detected in a drug test 48 hours after it was given. When long distance shipping, giving a shot when loading in the AM, I expect will effect the horse all day, to some extent.