Oh, I love
discussions like these. Let's see if I have this right: If you put on your coat before leaving the house, and wear it around inside before leaving, your body will start to think that the temperature with the coat on is "normal." So, when you walk outside into cold weather, it will feel colder than it would have otherwise. Plus, the assumption seems to be, you're from Arizona, so what could you POSSIBLY know about cold weather (given the San Francisco climate, many people would ask what SF people could possibly know about cold weather, but that's another story). You, perhaps cowed by strength in numbers, seem to have knuckled under, muttering to yourself but otherwise going along with the "local wisdom."
Well, of course the entire argument about getting used to the coat's warmth and feeling colder once you get outside is complete nonsense. I'll concede there is a tiny grain of truth in the "get used to it" hypothesis. To me, 40 degrees certainly feels cooler in August than it does in January, in part because in January I'm "used to" the cooler weather. But that's also because I've had several months to acclimate, whether to cool or warm weather. You're not going to make that swing in a few minutes.
In fact, you will actually stay warmer outside for a longer period if you wear your coat for a moment before venturing out. Why? Simple. You'll warm the coat to body temperature or close to it. Think about it. If you put on your coat the instant you leave the house, it'll be at ambient room temperature68 degrees, or thereabouts. But if you wear it for, say, two or three minutes before you go outside, the jacket lining will be much closer to your body's norm, 98.6 Fahrenheit or so. And it will take some time for the coat to cool down, ensuring a longer, warmer period for you.
So stand up for your right to put on a coat any damn time you want. Don't let those feisty San Fran people intimidate you.