For a system like this, I'd be wary of crating situations of degenerate gameplay, where some aspect of progress is gated based on the current season and the player has no choice but to wait around. This could be addressed with some mechanism of passing time quickly, or by not making anything mechanically significant tied to the current season, but that seems like it removes the impact and defeats the purpose. It's a hard design problem.
I'm not a programmer, but in my mind the seasons were more of an aesthetic change that gradually happens without really impacting the game, but gives the illusion of time passing. Either it would happen on its own, or it would be tied to a certain amount of progress in the game. In my mind, it wouldn't actually affect players' ability to progress. Just once you got 1/4 way through the game the season would switch or something.
It might not seem like it's very important to add when it has little impact on the game overall, but aesthetic features like this in games make me happy. It's just a small thing to add to possibly differentiate a game, and I think some players will go smile at the transition to fall, winter, and back to spring.
It's funny you mention Zelda, because Oracle of Seasons was all about this. It's pretty great. There isn't any passage of time in it, though; you just change from one season to the other with a special item at designated places.
This is sort of why I avoided mentioning the Oracle Games. Ages also has drastic time differences you can switch between, and it's interesting, but ultimately it's completely within your own control. To me, it doesn't really feel the same when it's something you switch between constantly and doesn't happen on it's own naturally like actually seasons/time. Also puzzles are tied to the mechanic. (To be honest, I own Seasons, but haven't played it much. I had to choose between Ages and Seasons as a kid and chose Ages because the box art was blue.)
I think it's really interesting to see seasons done right, but if there's a good explanation or design choice behind avoiding them, I think that's fine too. I'm currently making a game where the setting has a sky full of ashes and has been thrown in to pretty much a practically eternal (as far as the duration of the game goes) winter's night — not to avoid seasons easily, but because this is the specific setting and mood i want for the game.
That's the thing. I don't think players will really notice until it's actually there. So many games have gotten away without doing it, so I doubt many players care about seasons.
Another one I'm working on is going to have the character travelling up north throughout the game, with snow slowly creeping up along the way. Not a dynamic change, but a transitional one. It starts in a sort of autumn setting and eventually you're in a full-fledged winter wonderland with snow and northern lights and all. You're not going to be going back to the beginning in this game, so there is no need to double the assets and make an eventual winter version for the starting areas.
Awesome! Tying the seasons to individual areas of progression is a good idea, especially if there is no backtracking. I'll have to write that down.