I would hope any lesson horse that my (future) child would ride would not be spooked at all by low-speed winds... Okay, I wouldn't hope, I would demand.
When I was taking lessons, I got on the trainer's main lesson horse, and started to canter. He bucked (just a bit, and only once) on me. The trainer made me stop the horse, she got on and rode the crap out of him, and was very upset about that little buck. In her words, "He's my main lesson horse. He should never
do that." She was very, very upset. Turns out that there had been a hard, spiky bur buried deep in the saddle pad, and it had been rubbing on his spine. We always inspected the tack before putting it on, but this one wasn't completely visible, and we'd missed it.
Other than that one issue, we never, ever had any other problems. Lesson horses should be very, very safe. I'd question the safety of the horse in any kind of weather if the instructor doesn't think her horse can handle 10 mph winds.
What kind of horse is your son riding? Maybe the trainer knows her horses aren't completely bomb-proof, and is compensating for it? Either way, I would try not to get upset about one cancellation. If it happens again, I'd be a bit peeved. I've had my instructor cancel due to the cold, when it would have been just fine to ride. Usually she had something else that she really needed to do, and didn't have time to do it unless she cancelled. A bit disappointing, since I always look forward to my lessons, but not the end of the world.
Look at it this way: It saved you some money!