I have the same problem; very poor traction in the slightest amount of snow. The traction control kicks in and keeps the car on track, but the underlying problem, I believe, is just the tires. I bought my 2008 last November so I went through a NE winter with basically new factory issue tires and had the problem. I am looking into alternatives; maybe snow tires or good all season tires.
I have a 2008 Mazda3 5-door with traction control/ESC and it will NOT go in the snow. I’ve driven plenty of other cars in the snow, FWD, RWD, older cars without traction control, and never had such a hard time. The only difference I can pinpoint is the 17" wheels and possibly very poor stock “all-season” tires combine to make it particularly ill-suited for winter driving.