Do you do yoga or do you know someone who does yoga? You could knit them a pair of yoga socks. Others have told me these are great for dancers too. The heel and toe are open so that part of your foot can grip the floor but the rest of you foot stays toasty warm.
I found my pattern at Mary Maxim, but if your search yoga sock pattern you will come up with several different patterns. They are knit with regular sock weight yarn on 3.25 dpns.
Here is the finished pair. But when our 3 year old granddaughter saw them she said “The socks are broken”. Well they don’t look anything like her socks with heels and toes. Out of the mouths of babes!
Some of my completed socks: