I liked the idea of all players having the same season. I really don't think it should give VP for seasons.
How about seasons changing automatically after each round of turns? First each player has a turn in spring, then a turn in summer, autumn, winter last. Actually, that's what i expected when i read the topic. There would be cute possibilities for cards that are better in certain seasons, or cards that store cards for next season (putting them on your deck), or a Barbarian Ships that can only attack when the shore is ice-free, "Autumn sale" cards that cost less in Fall or Winter (after your opening turns)...
I think you can make it possible to advance the season, but that shouldn't be the standard situation. Maybe an expensive Event or something like that.
Edit: Oh, or even a supply pile with four different cards in there (not too different, a bit like Knights), where you can only buy each during (or outside) a specific season?
Edit 2: Or maybe have seasons take several turns, so they reflect phases in the game. Each phase could take four rounds, starting either in the first or third round of Spring (so cards better in Summer will start being better after your second shuffle and not be good opening buys usually)... Then you'd need a Mat/Board to track the progress, though.