Your car automatically adjusts your fuel to air mixture to be at at optimum level to balance power and economy. When the air is cold, it is more dense (essentially there is more air in each cylinder) so you need more fuel to reach that same balance point.
In a lot of small aircraft they don’t have automatic mixture control, you do it yourself with a pull knob. The difference in the optimal position of the mixture on a very cold day vs warm one in the summer is quite significant.
Air is more dense, takes more energy to push through. it will have more and more impact as speeds get higher.
Winter tires are softer and more aggressive. Good for traction, bad for fuel economy.
Snow and slush take more energy to push through.
Even spinning your tires at an intersection while trying to get going is taking energy that’s not going into forward momentum.
Edit: Also, when left outside all fluids/oils cool off and become more viscus. It takes more energy to push them around or rotate shafts in them until they warm back up.
The main cause is air density. Colder air is denser, which means it is thicker and causes more drag. So, the car has to deal with more drag, and you need more fuel to maintain the same speed and acceleration.
There are some other effects, such as the engine and powertrain taking longer to warm up – so there is more friction from cold parts and cold oil. If you do shorter journeys, this becomes more significant, and for very short in-town journeys, this could be the main effect.
What vehicle do you have? Type of propulsion?
Cold air should help a internal combustion engine, not the opposite.
The only reason I can imagine is: driving on snow or water or mud makes more resistance than dry tarmac.
Second if you have a hybrid car, batteries are heated because they can’t handle cold temperatures. If you have an electric or hybrid car, it will use some power to heat the batteries in winter and that has a negative effect on consumption. This is more marked on short commutes, given batteries are heated in the very first minutes of use.
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