Mittens don't need ribbing to stay on your hands - Enchained Mitts use the knitter's equivalent of a chain belt to decoratively cinch the wrist.
Mittens are worked in a worsted weight yarn - a great chance to use a variegated colourway - and then embellished with a bit of i-cord in a contrast fingering weight. The chain cording is a bit fiddly to work (it's attached to the mitt as you go) but the finished item is worth it. Using the shortest double-pointed needles to work the i-cord (4"/10cm) is strongly recommended.
If you have lots of sock yarn/fingering weight on hand, try holding two strands together as an equivalent to worsted weight for the mittens.