35 and rain is fine because it melts snow, as long as it doesn't freeze afterwards.
When I was working at Stop & Shop, I would sometimes take carriages from outside and put them inside. If I brought my heavy coat but not a light one, I would be fine in the 30s pushing carriages without a coat at all, although I would wear my light jacket if I had it. (Wearing a heavy coat makes me look less like an employee.)
There's also something called the clean sweep that requires checking certain rooms every hour (sometimes people would alternate), and one of them was the 5¢ deposit bottle room that required going outside and back inside. (There was an indoor connection for employees, but the door was typically locked, and it took longer, anyway.) One time, when it was 14°, I went in, scanned something, and went back out, without any type of coat or jacket at all. 15 seconds outside each way. And no, it wasn't 14°C.
My vote is for the kind that causes coughing.