You can run the mitten strings up through your parka sleeves, which works OK as long as you are wearing your parka all the time, as when it is very cold. If you don't run it up the sleeves, but have the string outside over your shoulders, then it is always catching on things, which can be a hassle.

In many situations, you will often want to shed the parka when working hard, like when humping up a big climb. In that case, the string through the sleeves also becomes a pain in the rear. You have to take your parka off, fuss with the string to put your mittens or gloves back on, then do the same thing when you get to the top in the wind and you want your parka on again.

An overall better approach, in my opinion, is to have a short loop attached to each mitten and put the loop around your wrist. When you need to use your fingers, you just slip the mitten off and let it hang by the loop. When you shed your parka, it is easy to take the mitten and loop off in one motion. If you don't want to wear your gloves at all for a bit you can clip the loops to a small 'biner on your pack so you don't loose them. Some gloves and mittens, like the last ones I got at REI, come with the loops already in place with a cordlock for easy adjustment around your wrist.