[Warning: Long post alert]
I often go 'wild' swimming and myself and my two girls have jumped into rivers off bridges and things all over the place.
The first thing is to put your arm in the water - as deep as you can as often the surface can feel quite pleasant but just a foot down, it can be very cool. Second thing is to take as much local knowledge in as possible.
For example: There's a bridge near Featherstone in Northumberland on the Tyne. There is a point you need to find on the bridge and it's quite safe and deep. This point gives you a clear 7 feet wide channel to jump in safely. With no prior knowledge, one would assume the middle of the bridge over the middle part of the river would be the safest but it isn't - there's rocks either side of the channel about 4 feet down. I would also get in the water first before jumping at a shallow point to see if the temperature is tolerable - as you slowly go deeper, you'll know straight away if want to swim or jump in it - there's no sudden shock.
I think that as we have had a pretty cool spring, a few hot days tempts people into jumping into quarries and lakes/lochs but large bodies of water take a long time to warm up, sometimes weeks, sometimes never. Like Loch Ness (never warm, it's deep), Loch Tay (there's shallow end that's beautiful but beyond that there's shelf and it' freezing). So when I go back to Featherstone in July, I am not expecting warm water and I will take my wetsuit and I will not assume anything.
That wetsuit for me is key - I do not like extreme cold but I can swim 50m in cold water without issue. It is also extremely buoyant. Avoiding strong currents even when the water temp is perfect is no no: stones are slippery and it's easy to slip. I always wear some form of footwear in case of cuts or slipping.
My youngest doesn't wear a wetsuit, jumps off the bridge and doesn't bat an eyelid, cold or not - she has a different heating system to mine. My eldest daughter wears one and when she was a baby, we went to the local baby and toddler swim sessions (water temp turned up to 34deg c), she would have a maximum 10 mins or her lips would start to turn blue. So each individual is different. I also think that kids are not nearly as active these days nor do they swim as much.
Getting hot in the sun, skin warm then plunge into cold water... it's a helluva shock.
View: https://www.youtube.com/watch?v=xmmAq4m6hE8
The above proves it is about tolerances.
Go in gently and if it's too cold, forget it.