I'm 41 and I don't wear socks. I wear sandals when I can from early spring until late October. In the winter I wear shoes that I can wear without socks. I live in PA,not as cold as Michigan I'm sure but still pretty cold. There are fur lined shoes out there that may work for you. Plus some boots you can go without socks. When I do have to wear socks or something on my feet I wear either nylons (if dress shoes) or, I call them Peds (that's the company that used to make them now there are more brands), they are those microfiber type "socks", they don't cover your whole foot just enough that your shoes won't rub the wrong way. I also like trouser socks (thicker than nylons but not like socks). Have you tried anything like that? If you have to wear sneakers for gym or sports that is a little tougher, you can try those peds. I have a microfiber pair I wear when I wear tennis shoes. Although I can't stand tennis shoes either so I wear ones that slide on (no back and no laces), and I can go bare foot in those. I can also tolerate (when I have to) those socks that have designs (like puppies, holiday designs, polka dots, etc), for some reason the seams don't bother me and this way they cover my ankles.
My daughter (9) also doesn't like socks. When she was 4 or 5 just like you she started to hate wearing socks. My husband used to fight with her to put them on until I told him to stop-he just doesn't understand. I let her go without wearing them and bought her fur lined shoes and fur lined crocs for the winter. But around 6 years old she developed hypohydrosis (excessively sweaty palms and feet) and her feet were too sweaty not to wear socks. I found her some she will wear. They are by Gold Toe, it's a sports type sock that is partly mesh and a very thin material. She has to wear them inside out because of the seams. The problem is I don't know if they sell them for older girls and grown ups. I hope so because she is in the biggest size in the girls department.
I would try to get shoes that you don't have to wear socks with. And try to find something you can tolerate for the times you do have to wear socks or nylons. Good luck.