It doesn't allow you to change the day of season
Yes it does! That's what the Season Length option is for .. the name is a bit misleading: it doesn't change the length of
all seasons, it changes how many days there are left in the
current season. So, if you move someone in and it's the 3rd day of Winter (2 days left in Winter) in the rest of the hood on that morning, you can set the season to winter and the length to 2 and everything is back in sync =)
Stupid Eaxis. Why didn't they just make it like that in the first place?