My ventilation page and cold coop page (the latter has more info on insulation, if I recall correctly) are in links below in my .sig, too
If single digits F is what passes for "cold" in your neck of the woods, there is no particular pressure to insulate unless you have unusually cold-sensitive breeds or want to run a heat lamp (although you should NOT need to). However, insulating can make things pleasanter and easier to manage, so if you happen to feel like it and run across the materials it IS a useful thing to do.
You can use fiberglass batts but if so you'd better be sure you have a real dry coop with no roof or wall leaks and no humidity problem. I like rigid foamboard insulation best for most (not all) applications; styrofoam board is ok too, and sometimes pieces can be gotten for free from stores that recieved them as packaging for merchandise. Regular styrofoam board makes more of a horrible mess if mice get into it than foamboard does though.
Yes, you need to cover the insulation with something peck-proof, most people use thin plywood or scrap panelling but there are other options. And your carpentry needs to be TIGHT -- no gaps or cracks anywhere -- to discourage mice from finding out what a nice habitat that is inside the wall there.
With insulation, in a moderately-cold or cold winter climate, you will be able to have more ventilation open more of the time (better air quality) without cooling the coop as much. And if you should be one of the people who runs a heat lamp, whether or not it is strictly necessary does not matter here, you will be able to use a lower wattage and/or have it on less of the time, both of which will save you money AND reduce risk of fire.
That said, unless you have unusually frost-sensitive breeds you can certainly go without insulation. You do need good ventilation all winter though. Don't be tempted to shut the coop up tight to try to retain heat, that results in humid air and thereby frostbite at relatively mild temperatures.
Good luck, have fun,
Pat