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.
My understanding is that tropical regions tend to divide the year into "wet season" and "dry season".
I've also always thought that the equinoxes and solstices should be the middle of the seasons, so using the 'cross-quarter' days as the beginning of seasons makes more sense.
probably same for other post-soviet countries too?
But we lost a lot of nice symmetries that way, which is unfortunate
Summer doesn't work with that association though, with the latest sunset being the end of June instead of the start.
You do realize there's also a southern hemisphere on planet Earth?