If the intention was for Spring to not be seen again, then I don't see why 20 was chosen, since plenty of games go past 20. I thought it was more intuitive that you'd want to see Spring again, because you're obviously not going to play the cards in the first two turns, and that leaves Spring in basically t3-5, meaning any card that mentions Spring with the 20 turn system either needs to be an opener or is just irrelevant, and I don't think that's smart design wise. In fact, I think it would be more interesting with an approach that does see Spring again most games, it makes that season relevant and is kind of nice thematically. If its 20 turns, then Winter effects are just going to be sad in general because most games you'll just never see them. So I don't see why making two seasons virtually irrelevant is worth ensuring seasons don't double up (which honestly doesn't seem that big an issue anyway. I'd rather expect to be able to see at least an entire season most games than just expect to end around Autumn). However all that said, I can see the argument for 16 turns, since that's just a bit longer than the average game at 15.5 turns.
Anyway, here is my first attempt at a card (built for a 12 or 16 turn season).
No idea if this is balanced, still testing the waters a bit. Not sure if seasons as a whole should be stronger or weaker than their each individual effect. I went with strongest in winter/autumn and weakest in spring/summer here.