Doesn’t this defeat the point of taking your shoes off inside? If your concern is tracking in dirt or germs on your shoes, tracking them on your feet is arguably worse unless you’ve got foot wash stations at the doors.

My feet are kept warm by keeping my house at a temperature where I am comfortable.

I think I’d still just go barefoot personally. Socks aren’t bad, but shoes for carpet kinda misses the point of carpet IMO.