I never run the shower until it's cold.

Therefore I never drain the hot water tank. Therefore it is never really cold.

So what happens is the hot water temperature dips, the thermostat cycles, and it heats the tank back up.

Hot water tanks are usually set between 104 F and 124 F, let's say an average of 114. Water supply in my area dips as low as 45 F in winter, may be as high as 80 in summer.

I would agree that 45 F water is cold and if you drained the tank completely you would be heating cold water. But that doesn't happen; you are always heating a mixture and most of it is hot.