With their smaller body mass a 10 year old will cool down quicker than an adult. True even in warm waters. Better to have them happy for the day than getting cold half way through a dive and wishing they had not done it.
Kids will sometimes let themselves get chilled so the adults have to watch out for them. One of the things they caution about in teaching/leading kids.
Sort of on the same subject. As parent of a young diver it is imperative they have gear that fits, maybe even more so than adults. I have now outfitted my kid with gear because of a bad experience we had when she first started diving.
We were going to Catalina Island for the day as a family and decided since my oldest daughter and I dive it would be a great opportunity. She and I would go diving, wife and other two kids would go explore the island themselves. I booked a DM to guide us because this would have been her first dive after certification. The scuba shop I used repeatedly told me they had gear for kids and they would be able to fit her with a full set wetsuit, fins, mask, etc.
When we arrived about the only piece of gear that fit or was appropriate was the wetsuit. They didn't have hood, gloves, or booties and put her in a full foot fin without booties. In hind sight I should have thought it out and at least had gloves and booties since those are required for my OW certification in California (she certified in the Caribbean while on vacation). Meanwhile, the DM was in a dry suit and I had my 7mm with my own hood, gloves, and booties. Poor kid got so cold after 30 minutes she was almost shaking when we finished. After about a 1 hour surface interval it was time to get back for the second dive. I took one look at her face and saw the apprehension about getting back in the cold water. I decided to thumb the second dive. Wasn't going to be worth the dive if she was going to not enjoy it because of the cold.
Upon getting back home I scoured the internet for sales and now she has mask, fin, gloves, hood, booties, wetsuit, and BC. She will be getting my computer when I get a new one and we still rent the regs for now. Her comfort level and enjoyment has increased with her own gear. I did have to replace the first wetsuit this Christmas since she has grown. New one fits much better and no longer chokes her in the neck. Best part is she now wants to try it out which means I get another chance to get in the water!