If you spent a lot of time outdoors, with poorly protective clothes, yes, you would want to eat more calories. When your cold your body shivers to increase body heat. This causes more calories to burn than if you were inside a warm room. But since we don't typically spend a lot of time outdoors in the winter (which is why you're more likely to get sick, by the way), and when we are outside, we bundle up, the increase in shivering isn't enough to cause you to burn significantly more calories, so you don't want to eat more.
In the summer, a different effect occurs. Being outside in the heat causes you to sweat more. The weight loss that people tend to see in the summer is primarily from dehydration, which can be deadly. And that to the increase in exercise from playing around outdoors, and you can see where it's easier to lose weight in the summer than the winter, when we're more stationary.