At what temperature do you restart a swimming pool?
I guess you are asking about daily air temperature. Once the surface has melted, the only concern is the above ground pipes freezing. If you leave the pump running all the time, the chance of freezing is very low.
Why is it when it's raining the water in the swimming pool is warm but when it is sunny the water in the swimming pool is cold?
It's all about how your body reacts to relative temperatures. The truth is that the pool temperature is not likely to be the culprit. It's more about how your body perceives the difference between the outside temperature vs the pool temperature. The transition from standing in the hot sun to getting into your pool makes the water feel colder than it might feel than if you are standing in cold rain before entering the pool.
Everything has a minimum temperature including all swimming pools. If you mean minimum usable temperature, that would depend entirely on the person using the pool. Most people think 68 degree water temp is too cold to swim in, but I have gone swimming in outdoor pools with water temp in the mid 30's to patch holes in the pool liner. And NO, I didn't have a drysuit or wetsuit available to use on that job…