The first few hours of Forza Horizon 4
see you experience all 4 Seasons before you join the full "shared world".
As you complete races, challenges and other activities you earn Influence. This Influence is used to fill a progress bar which you see on your Map from the main menu, or as a pop-up while you're driving.
Fill the bar to reach Horizon Autumn.
An extra note from the comments:
I suggest noting that the achievement doesn't pop right away after you fill the influence bar. You need to do that, then buy the first house. Doing that gives you your first chance to change to new clothing, and after you exit from that, the achievement pops.