However, the definition of "season" is a period beginning at solstice or equinox (and ending at the next equinox or solstice; that is, at the start of the next season).

Well that's entirely my point. Who "defines" this? I'm complaining that such a definition is sometimes used, with obvious absurdity.

For me, my winter is the period of greatest cold, which is more or less evenly distributed around midwinter (in my case mid-December). This seems the natural definition of a season. It's winter when it's most wintry, and it's summer when it's most summery.