Wow, I thought this was a perfectly appropriate question. Give the guy a break, seriously. Is this how you'll treat your patients when they ask a seemingly stupid or naive question?
At Pittsburgh, they gave us a room to put our stuff in and it was locked--this was mentioned in the interview letter so we could anticipate it. If there's inclement weather, you'll likely not be the only one wearing a coat that needs to be stored somewhere. I'm sure the school will accommodate you. At UNLV and Midwestern, there wasn't an official area to put stuff, and I only had a laptop case, but there were plenty of places/rooms to put stuff should people need to.
Dress how you feel you need to. The faculty at the school are still human. If it's raining or snowing, they're not going to look down upon you for wearing a heavy coat or bringing an umbrella. If they do, don't go to that school--those aren't the kind of faculty you want to be around. You'll be okay, whatever you do. I know it's easy to freak out about every detail, but just act normal, and think normal... it's not (or shouldn't be) a sub-human experience.