I've watched a lot of people shiver lately. I asked a friend if she has any cashmere sweaters. She said she has two. I asked why she wasn't wearing one today (she had on several layers, her jacket over her shoulders and my jacket in her lap, my scarf wrapped around her hands). She said, well, I'm wearing...she plucked at the sweater she was wearing, and said she was wearing layers.
It isn't cold for long periods here so people don't really figure out about wool. It's warmer than cotton.
If it were cold longer, I'd replace my silk underlayer. LL Bean has some. It is thinner than long underwear so clothes still fit. But the silk layer a little larger than skin tight so you don't rip holes in it just putting it on.
But a layer of silk, then cashmere, and then anything and the body stays warm. I don't need all those layers here. If I were outside and not active, I would, I guess. But the shivering people I'm seeing aren't even outside; they are in heated buildings!
Get wool. Wear it. Take good care of it because it isn't cheap.