My '04 Civic has NO traction in winter. Why?

I have 15x6 rims (wider than usual on a Civic), which means wider tires. Last year I got stuck on a 1-2 degree incline and couldn't budge it. My tires DO have plenty of tread left. I've heard that having narrower tires on during winter helps with traction. True? And would a smaller diameter tire also help? Thanks!