First, the power the run the fan is minuscule. On the order of a few Watts. Maybe a few tens of Watts at most. It's an order of magnitude less than what is needed to run seat heaters (and those have almost no measurable effect on a Model S's range, which is why "range mode" uses seat heat in favor of air conditioning). The energy use you're talking about is enough to move the car an extra few hundred feet after a multi-hundred mile drive.
Second, every ICE has a thermostat on the radiator. It greatly reduces coolant flow to the radiator when the car is warming up, or any other time that the coolant is below optimal temperature. I spent many years in the northern (continental) United States and never encountered a situation where the coolant temperature gauge on an ICE car failed to show normal operating temperature after 10-20 minutes of warm-up time.
The cold-weather fuel economy difference in a conventional car mostly comes down to greater air density.