Yes, Generally cooler requires richer setting
Here is one theory: The cooler air contains more air molecules per cubic inch (the air is denser). So to keep the mixture about the same you need more fuel too. So you open up the needle valve in colder weather.
Really you need to be able to get this right regardless in any weather. One of my favorite techniques is if you can get access to the fuel line while the engine is running at full throttle, pinch it off either with your fingers or with a needle nose pliers. The engine should speed up somewhat before it dies. If it dies immediately it is too lean.
Another technique, even easier, is to hold the plane straight up and open the throttle to wide open. the engine should pull at least as strong in this position as it does when it was level. If it sags or quits it is too lean.