Winter is "officially" supposed to begin on 21 December, and spring on 21 March. I think this is ridiculous, and has little to do with the real world, nor with the earth's orbit (21 December is also the winter solstice, so is in the middle of the "orbital winter").
As an ecologist, I prefer to look at what actually happens in the countryside (in the UK at least).
Winter is when plants are generally not growing, and deciduous plants have no leaves. Down here in the soft south, usually from mid-November perhaps to mid-March.
Spring is when everything is growing, but little is mature -- the leaves are not fully expanded, the birds are beginning to nest. Round here from early March to early May.
Summer is when everything is mature, green and growing. May to September or so here.
Autumn is when everything is shutting down for the winter, summer birds go, winter birds arrive, leaves fall etc: October & November.
There is quite a bit of overlap, really, even in one place. Blackbirds may nest in February, while swallows don't start till May; swifts and nightjars leave in August, swallows perhaps not till October.
Everything is different further north, or indeed south -- not least in the southern hemisphere... And it's changing with global warming, and varies with the weather.
So it all depends upon what you really mean by "winter".