That does sound like a different kind of tri. First come first swim? New one to me. And a mass bike start. Interesting as well.
I did a tri last year... where it was 35-40 degrees with winds blowing up to 30 mph. We didn't have the luxery of changing into dry clothes.
I basically put a towel by the exit... dried off on the way to T1... then in T1 I put on cycling pants (not tights), a jacket, a hat and full gloves. I raced like that for the entire race. Oh, and I had the most clothes on of ANYONE out there. There were guys and gal in just their tri shorts and tops racing. Bbbuuuurrrrr.... no thanks!
So, the fact that you can actually dry off and change... you are lucky. I say just pick something warm and easy to put on.
Good luck!
"Life is not a journey to the grave with the intention of arriving safely in a pretty and well preserved body, but rather, to skid in broadside thoroughly used-up, totally worn out, and loudly proclaiming: WOW WHAT A RIDE!!!!"