Winter is approaching. It gets cold here. Cold water. Would the cold water shock the roots of the plants or not?
Very cold water can shock some plants, especially if the surrounding temperature is warm. You didn't mention where you are, but in most large cities, water has at least some chlorine in it, which is a growth inhibitor.
It's a good idea to let water sit in the pot for a couple hours or more to let it get to room temperature and to allow chlorine to evaporate before watering your plants.