I would say "it depends"
One of the things I really pay attention to when I move stables is who will be handling my horse. I have found that age is not so much the issues as personality.
There are a LOT of barns who use teenagers working off part of their horse board for general chores. Kudoes for making that work out.
My point here is that a 30 year old person who is afraid of your horse can screw it up a lot worse than a 12 year old who is not. I have seen many people trying to move a horse from point A to point B with a horse that is too much for them. Although once might not be a problem, daily is a disaster.
My horse will test a person, though he is ALWAYS the favorite horse as a stable because he is pretty and a complete dork fish who will do anything for attention. He is safe to allow toddlers to brush his legs or ride alone on in the arena under supervision - as long as they are happy with where HE wants to go. This does not mean that he is beginner safe and absolutley is terrifed of a man with a harsh attitude. I have actually gotten phone calls at 10pm because the stable owner (mid 30s) was afraid to put him back in his stall.
Without a firm hand, he is a bully, with too strong a hand he is up in the air striking (has only happened twice in 13 years, so I can only guess what they were doing to him when I was not there). He also prefers women to men.
Because he is such a BiPolar critter of bombproof one minute and poke poke the next, we have gone through about ten stables to find one where the manager works well with him. She is in her early 20s, and puts him in and out every day. She will let the kids who are also around put many of the others in and out, but not him or two of the others. However, she is not comfortable with the two year old filly I just bought my daughter, who was only barely halter broke when we got her a few months ago. We will have to see if that deveolps into a problem.
Another thought to watch for, is if the stalls are being cleaned with the horses in them, a lot of people who are afraid will smack the horses with the rack, which for a sensitive horse is pure mental torture.
So... I would be more concerned with watching how the person who puts them in and out interacts with them then how old they are. The reason I bought this horse was because my eight year old did everythign with him - and he was stil a stallon then. It is not age, but love of horses, respect for them, and inherant knowledge when to tell them to knock it off that makes it work or not.
Soggy in Seattle