Sounds like the thermostat is stuck open, at least partially. Going downhill means the engine is under less load and isn’t generating as much heat and because it’s colder weather, dissipates heat more quickly. In warmer weather, the open thermostat allows coolant through the radiator at all times rather than when it’s supposed to at a certain temperature. This very same condition happened to me about 3 weeks ago, just in a different car. Cooled off going downhill and all.
I should clarify that the car had a mystery drain I could never find, and I added the switch to cut off the battery so it wouldn’t lose its charge.