Comment by perilunar

That's how it works in Australia, though rotated six months: Summer starts December 1, Autumn starts March 1, Winter starts June 1, and Spring starts September 1. I think it even has legal status. In the North of the country though they typically just use wet 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.