Ocean currents, elevation and distance from the equator also have a big impact on what the season is going to feel like.

There's no need to change the dates. They're already arbitrary based on the position of the sun and the earth and people have the experience to take them with the grain of salt necessary to the region they live in. People who live near the equator probably don't have much care for the notion of the winter at all. Folks who live far up north know that spring actually comes in much later than march 21st. People who climb glaciated mountains in the canadian rockies know they won't get summer conditions until late june.