So as winter is starting to hit across the country and actually produce snow I have started seeing mittens, hats, and scarves across town left in snowbanks and lost&founds due to children dropping them or taking them off when they shouldn't. I know alot of people have issues with this and though I'd share a couple strategies I've used through the years to help.
1. Mitten/glove keepers-they sell these commercially lots of places (I just saw them in the bargain section at Target). A piece of elastic is set with aligator clips on both ends to snap onto the coat sleeve and the mitten so that even if they take off the mitten it stays on the coat. They can be pulled off, but this usually takes enough force to tear the coat and then you might want them to fall off as you child could be caught somewhere.
2. Extra buttons-I sewed a button onto the back of a coat on the outside in the middle of the collar back and made a button hole in the scarf. The scarf can then be buttoned onto the coat to lessen the chance of loss. Button holes are pretty easy to sew by hand but a machine is easier.
3. Cubby bins-used for storing when you get inside. Each child can have their own to store hats/gloves/scarves so they don't fall out of the coat as they are putting it on and get trampled or fall out after they hang it and get wet/soggy.

The one thing that I will say is do not tie mittens together. The old style keepers used to have a cord that went from one mitten to another through the sleeves.

They are a strangulation hazard and should not be used.

Those are great suggestions. My kids are big enough now that they are pretty good about keeping track of their stuff, thank goodnesss. When they were little I bought little tags printed with their name and phone number. I sewed these on everything. Then when someone finds them they can call you. It also made me feel better that if my kids ever got lost they had their phone number with them!