The “You run in this?” query comes more often in winter than summer. But running in sub-freezing temperatures isn’t really that big of a deal after the first 10 minutes. By then blood flow to your muscles is significantly increased, and you feel a lot warmer. I always dress for what I’m going to feel like 15 minutes into the run than for the first few steps out the door. I’d rather be a little chilled at first than be weighed down with extra clothing half an hour later, when I’m moving well and probably no longer thinking about the temperature.
The exception for most people is their hands, which seldom warm as much as your core. But they do usually get a bit warmer, and mittens can sometimes make your hands start sweating. I have a pair of gloves with a fold-over mitten flap that’s the perfect solution for this problem.