I've commuted on the drz all the way through winter, in January my rides started before the sun rose, so about as cold as it gets in AZ.
Being a poor HS student, I found that layers are they key. I found one of the most important layers is a long sleeve Under Armour shirt (the tight kind). Then various layers of light cold weather gear depending on how cold. Then a riding jacket, then the second most important, the windbreaker. I found without either the windbreaker or Under Armour I was freezing no matter how many other layers I had. The windbreaker keeps the cold out, Under Armour keeps the heat in. Same concept with gloves, I had some of those small cotton gloves, as well as big poofy winter gloves.
That's my experience, maybe an electric vest would be better, so you don't have to have 5 layers of cold weather gear
but I found that I was fairly comfy with what I had said above.