Does milk (fat) change in Winter?
I don't know about weather, but non-factory produced milk changes with the season because of the feed, which will affect your butter.

Over the winter, the cows are fed hay or corn, while over the summer, they're pastured, so get fresh grass.

In the Netherlands, there are designations such as 'graskaas' (literally, 'grass chesse'), which is made from the milk when the cows are first released to pasture in the spring.  I know there is a designation for winter vs. summer cheese as well, but it's not coming back to me.