I hate coats for many different reasons, but I now understand the need for nice looking outerwear. When I see Olivia patrolling the city streets in various lengths, colors and styles of coats, I'm reminded that coats can really enhance a look, or ruin one when they're not quite right. Take some notes from Olivia, then fill the several empty hangers in your coat closet. I didn't realize how many coats a person really should have until I moved to Chicago, (short, long, casual, formal, sort of casual/sort of formal...my head will start spinning) and though they're not cheap, they last and are an important investment. Once you get to a certain age or stage in your career, that slightly too small puffer coat that doesn't quite cover the bottom of your blazer or cardigan just doesn't quiiiiite match your sophistication level. Or at least the one you're trying to convince people you have achieved.
Olivia is always well-equipped for any level of chill, and her coats always look nice with her outfits. They're long enough to cover whatever is underneath and they can trick someone into thinking they are actually part of her outfit, which is the key. Whenever you get a coat, it should be versatile enough to wear with several different outfit combinations. Shorter and longer nice coats are extremely important for wear over both dresses/skirts and pants, and the neckline of the coat should complement the type of clothes you usually wear. If a lower cut neck opening adds confusion to your look, get one with a high neck closure. If you have an abnormal waist and a belted coat doesn't look quite right, get one that's well tailored using buttons and darts and ditch the belt.
Most real humans don't need quite as many coats as Olivia, but she has such a variety and wears them so thoughtfully that it's a good idea to use her for guidance and to kind of shop a look for you. If you're meeting someone new during the colder months, the coat is their first impression of how you present yourself, so make it as good of a choice as Olivia always does.
Shop some Olivia look-alikes for her feminine, structured and indulgent outerwear look. Try this, this and this for some similar looks (I'm pretty sure that trench is one she's worn on the show). And if you can't get her Burberry duplicate, Gap has a worthy reasonable alternative.