Not just a visual winter, and not a Aquilo-style freeze - dynamic seasons come to Nauvis with moving snow and thaw fronts, freezing lakes, increased factory energy consumption, heating, and mineable ice
The map takes 8 hours to traverse by foot, so the wave can't really start at the edge of the map or it would take forever. I'm asking because I'm curious.
The snow front moves at roughly walking speed. So in your case, it would take around 8 hours to cross the map horizontally.
The season durations must be long enough for this. If there is not enough time, the snow front will stop, and a reverse front will start moving back from the right edge of the map.