Bani.- yes yes yes. This is always my issue too. Admittedly, I have been known to be in the cty in a dress and heels with a coat, leaving my lower legs exposed. But I hate it.
Having said that, my smart work wool cost, purchased years ago for an eye watering amount of money (for me - £495 but I was working in investment banking at the time so it seemed like a legit purchase), is fab and I love it but to be honest , I've always been surprised by how it isn't terribly warm! I thought wool coats were the thing! So I still use it but if I need actual warmth, I'm wearing my puffy coat with thermal leggings under jeans!!!