Cosy used to mean one thing: a jumper that made you look like you were hiding from the world. That has shifted properly in the last few years, with knitwear, layering coats and soft trousers all cut with more shape, so you can be warm and still look like you dressed on purpose. Mostly a good change, though the shapeless version still turns up if you're not paying attention.
Before you buy anything in this category, check the weight of the knit and where the sleeve actually ends, because a lot of "oversized cosy" jumpers are cosy on the hanger and then swamp you the second you sit down, sleeves past the knuckle, body pooling at the hip in a way that reads as borrowed rather than chosen. With coats and gilets, look at where the zip sits when it's done up and whether the arms allow for a jumper underneath without pulling at the shoulder seam, that's usually where the cheap ones give up first. Soft trousers and wide leg knit bottoms need checking at the waistband too, elastic that's generous when you try it on in a warm shop can tighten up the second you're sat on a cold train seat, so if in doubt go up rather than down.
On colour, the easiest things to live with are the ones that don't shout, so soft browns, oatmeal, deep green, and a proper burgundy rather than a bright red, all of which forgive a slightly worn finish and don't date the way a trend colour does after one winter. If you're starting from nothing, the single piece to buy first is a mid weight knit in one of those shades, not too chunky, not too fine, because it layers under a coat in October and works alone by a radiator in March, which no single cosy item ever quite manages to do in both directions at once. Pair it with the plainest trousers you own and the whole thing already looks considered rather than thrown on, and once that's working you can add the gilet, the scarf, the soft cardigan over the top, each one earning a reason to exist rather than just adding bulk for the sake of it.
Wash knitwear on a cool cycle and let it dry flat, hanging it will stretch the shoulders out of shape faster than any amount of wear will.