My secret to good, really really cold water at home:
Clean two old gallon milk jugs very well. Fill them up about halfway with tap water and stick them in the freezer. When they’re frozen, take one out, fill it with tap water, and keep it in the fridge. Refill it as needed until the ice is all gone. When it’s gone, refill it halfway again, put it back in the freezer, and pull out the other one that’s been waiting all nice and frozen.
We used to do this all the time when I was growing up, back before fridges came with ice makers and chilled water dispensers. When we finally got a fridge with those newfangled gadgets, I was sorely disappointed that the “chilled” water wasn’t nearly as cold as I was used to. Now that I’m on my own, in an apartment with an old fridge, I’ve gone back to the good ol’ way of doing things.