Your cooling system should be able to let your thermostat regulate the temperature of your car in all driving conditions with some reserve cooling ability. Otherwise you risk overheating.
The point of the thermostat is to set the minimum operating temperature. That's it. It's only purpose is to keep your coolant temperature above that minimum setting, so when you're driving around in cold weather you don't damage your engine. It should have little effect on the actual operating temperature most of the time, and it has no effect whatsoever on the maximum temperature.
Temperature regulation is up to the fan system and the radiator, and conditions absolutely matter. On the freeway in the cold you're depending on the thermostat to maintain that minimum. The rest of the time you want your operating temperature to be maintained by a combination of the radiator and air flow, whether the air flow is being set by the speed of the vehicle or the fans. The worst case scenario is the car running, not moving or moving slowly, with all of the air flow being created by the fans. If the fan(s) can maintain a set temperature when doing that, there's no risk of overheating.
