"It sounds to me like many of you consider them as part of your outfit": Fashiontern, yes, that's what it is really, when you live in a place where you must put a big coat on everytime you step out. Then, most interactions happen with your coat on, even inside, as we walk in and out of places. Getting your kids at the childcare (in &out), grocery shopping (in&out), walking from parking to building to office (often, in&out), coffee shop, school, errands, public transportation... In winter, in an urban setting, the main problem is feeling too warm because it's not convenient to remove and hold your coat (it's simply better to keep it on). And in colder climates, you do need a tougher, bulkier coat. Really, at this point it shouldn't be called a coat, but "gear". An item so bulky that if it's not on you need two arms to hold it (my special thoughts to young parents standing in line to see Santa in shopping malls), not to mention the pesky accessories that tend to travel in all directions, oppositional defiant hats and gloves suddenly slipping away between the folds of the coat or lazy whinny scarves ready for a nap pulling and dragging behind as you walk. And in restaurants! You almost need a full seat just for one coat (think Baymax from Big Hero 6). In short, going out in the winter demands serious organizational and management skills.
You are lucky to dispose of the luxury of considering your inside winter clothes as your main outfit. When I lived abroad in warmer climate, I thought this was an incredible booster to one's quality of life. People don't realize how fortunate they are to be able to throw on a relatively speaking lighter coat as an afterthought.