In the case anybody else is interested, season did change at in-game midnight. The last day of season was marked "0 days remaining", and the first day (of Spring) is marked "29 days remaining".
In-game days.
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Also, I see that a new year has started... and it's Day 0 as programmers are used to count from zero.
Maybe, for those who do not know the joke, it would be better to name the first day the first, not the zeroth? And now I start to think there was something like "Year 1" earlier, no?