Some children get cold quickly, too (indicator: blue lips), or maybe you go places with colder water. There are wetsuits for children too.
Additional pros to kids' wetsuits:
I inherited one from a cousin when I was small, and loved it.
Note that there are also different thicknesses. For water that is only slightly too cold, wearing a thinner stretchier wetsuit is often cheaper, more comfortable, and more effective at minimizing water flow. Water flow is also a reason to prefer a wetsuit with more coverage, and tighter/fewer inlets. Long sleeve > short sleeve > vest. Also, I would recommend taking the wetsuit off and drying off once it of the water unless you plan to go back in soon. When surfing in NorCal, I used to bring a big jug of warm water insulated with a towel. After surfing, it was a good way to rinse the salt water off of me and my wetsuit, and also warm me up enough to ease the process of taking off the wetsuit and toweling off.
Oh yeah. A wetsuit helps me immensely as well - I just lose heat too fast otherwise. It turns a chilly experience where I have to keep moving all the time, into a nice relaxing thing.
I get cold very quickly in the water, enough that unless it's close to body temperature I get chilled through within ~15min. This mostly wasn't a problem, because I'd take a quick dip to cool off and then hang out on the beach, but now that I have kids they (and I) want lots of swimming together time. When I touched on this a few weeks ago people recommended trying a wetsuit, and yesterday evening I did for the first time!
It was different in a bunch of ways, but on balance I like it a lot. Some things I noticed:
Initially there was some air in my suit, which felt funny bubbling out.
The suit is slightly buoyant, taking some getting used to.
It still felt cold getting in, until my body had time to heat up the trapped layer of water.
I didn't get cold in the water! This was with maybe ~78F water and ~82F air. I could play with my kids until they wanted to get out of the water.
I bought separate pants and a vest, which I wore under my swimsuit. The pants worked very well, and the vest worked ok: I got a bit of water rotating through where they met, and I occasionally needed to pull the vest down. Possibly a full body suit would have been better? But those seem more annoying to get in and out of, and the amount of water moving through was pretty low with the kind of playing we were doing.
Once I got out of the water, I stayed wet a lot longer. This was warmer than usual for the first part, since it was a warm sort of wet, though after we got to the stage where I normally would have been fully dry (~45m?) I was mildly colder.
Overall I'm happy, and am looking forward to swimming with it again in the future!
(My kids are now asking if they can get ones too, which is fine with me!)