Thick dress socks?
I wear Goldtoe Uptown Crew socks. They're mostly cotton. I find the best deals on them at Kohls. Amazon has them for $17 for a 3-pack which is OK but not a great price.
A vast majority of shoes are only comfortable for me with a cushioned sock, which is unfortunate as most good looking socks are thin.
When I described the Gold Toe Uptown Crew socks as "cushioned" I just mean they have the thickness in range of an athletic tube sock which cushions the foot. However, these Gold Toes have a smoother texture and look much more refined than an ugly athetic sock. They're still a good bit frumpier than the nice dress socks people tend to sport on this forum, but they're not awful. Sometimes I think they kinda fit into the trad aesthetic, which makes me feel better about them.
Docker's "Sport Crew" Socks might fit the bill... I typically wear 'em with boots, but won't hesitate to wear them with shoes in colder weather. They're definitely thicker than dress socks, and the colors aren't too bad: I especially like the the "Dark Marled" mix-pack, the black is good too.