You're right that it doesn't look like a February climate but the seasons in which the shows were filmed aren't always consistent with the dates of the episodes (ex. "Somme/Trenches of Hell" in early August with
snow on the ground!)
Since the title card for the original episode says "Princeton, February 1916" and Indy's stint in Mexico is definitely March, the climate has never been an issue for me. There's nothing substantial in the new footage to suggest that much time has passed between the Edison adventure and the bridging scenes.
Because of the trees, clothes, etc., I can see why you're thinking September but the fall wouldn't make sense with the story. What has always puzzled me* is how the junior prom could be in February?
If one wanted to, one
could argue that the chapter in question takes place in
May 1915!
*I didn't grow up in the American school system.
Great talking to you. Will get back to that soon enough in the Old Indy thread!