Apples can get only autumn, berries - summer, mushrooms - summer/autumn, eggs, flowers - all seasons but winter. All wild food can take only from apple tree/shrubs.
I like this idea.
There are spring mushrooms, grains can have two harvests, etc.
There are a bunch of things to consider when creating ecosystems; for example, I just wouldn’t let grapes grow under New England’s skies, because they yearn a temperate/warm climate. Since this system is not wrapped around fictional flora or fauna (at least the off. canon isn’t) it’s much heavier to predict everything about individual items.
Another thing - try “Everything’s Suddenly Blooming!” once the carbon-monoxide/dioxide emission hit bottom low, and now you’ve got only armies of evil to breathe and eat those berries with. 
If one were to make apples grow reasonably similar to real life, one would find springtime or even summertime forest survival to be a lot more uncomfortable - as apples can be crafted (smushed) into a safe drink. I know there are some other recipes that help with quenching thirst, but if there are no water sources within reach, apples are amazing early game. Or if you’re like me and like to not be reliant upon cities and have shite luck finding rivers before dying.
I like realism but I suspect the tradeoff is you’d start to see players with huge starting-season preferences. This might not be a bad thing. Kind of reminds me of season-picking in Oregon Trail.
Concord grapes (and their wild progenitor, the Fox Grape, Vitis labrusca ) are well known to grow in New England states.
I guess I was just trying to make a point; the real mennace behind the weather/climate system should know best.
I don’t even see a real point to this, other than respecting Reaper’s insight; but we all do love yumyums.