This is silly. The fish are producing the ammonia constantly. They don't say "ah, it's 10am and I gotta sit with a paper and bust my daily loaf".
The filters are able to keep said constant supply of ammonia in check on a continual basis to the point where we're unable to measure the ammonia level with our hobby-grade test kits. In a cycled tank, ammonia doesn't build up over the week (or month or whatever), it stays at zero.
This means that if you have two tanks, same size, same stock, same feeding, and change water daily on one but only weekly on the other, both tanks will have exactly the same amount of bacteria in the filter. The bacteria multiply to the point where there are enough to handle the ammonia production. There are no more and no less, regardless of how much you change water.
Oh, and really cold water isn't a "regular water change", it's an attempt to kill your fish.