Hi Fancy! I think the size sounds fine, I rode plenty of horses that size when I was younger. What you want to look for is a calm, polite horse. How to see this is:
the handler asks the horse to move away, the horse does. Make sure the horse doesn't crowd, nip at or try to bother the handler. I absolutely agree with the earlier advice, watch the owner (or regular handler) get the horse, groom, tack and ride. This will give you a chance to watch how that horse gets on without the stress of riding it.
Does the horse accept the bridle and saddle?
can they clean all hooves? can the touch the horse anywhere?
Will horse stand quietly or dance around? is the horse a pocket seeker?
Also, when the rider mounts, does the horse stand, walk off during mounting, put his ears back, swing away from the mounting block? These last can be back issues, or a poor fitting saddle.
While riding, does the horse submit to the rider, does he swish the tail a lot? does he respond,or does the rider need to urge him forward, or haul back on him? Does he wear a mild or harsh bit? do they use any other equipment than a saddle and bridle? Why?
do they use a whip? Does he turn, stop, speed up and slow down? Will he stand quietly? (very important for having the Instructor talk to you, or gossiping with friends!)
Can the horse do what your DS wants to do? Ask the owner to show what the horse can do. Ask how much food, any special feed/meds/ect. Has he been to any shows, events, or off the property?
If the horse seems dull, or bored, not interested in anything and plodding around, beware of sedatives. If the horse is particularly thin, beware that once it has weight on, it may act up more.
That's my advice!