Max, While the Prius is certainly not an SUV I thought it handled adequately in the recent snowy/icy condictions here in the Wash. DC area. My previous car was a Grand Prix with Traction Control and ABS which wasn't bad but I had to make use of the lower gears; the Prius definitely handled better. This may be partly due to the extra weight of the batter towards the rear of the car and the ability to apply power very gradually with the Hybrid system. I used to prefer a manual transmission in the snow but with the "continuously variable" tranny of the Prius I had no problems whatsoever other than having to maneuver around other vehicles that should not have been on the road.
We just got ~6 inches of snow last week on top of an icey base. I was concerned since the plows had not gotten to my street and I'm on a steep hill. I was very pleased at how the Prius handled. Going downhill the traction control engaged once briefly, but I didn't have any trouble at all going up or down the hill. There were quite a few accidents that day. I think the Prius handled better in the snow/ice than my 1993 front wheel drive Subaru Legacy used to.
With all season tires, it's much better than the 2001 Prius if that means anything to you. I'd say that it's better than average for a mid-end front-wheel drive sedan with all season tires. Clearance isn't the greatest, but of course, the Prius isn't a truck. The Prius with all seasons certainly wouldn't have the traction of a four wheel drive vehicle with winter tires obviously, but I'm happy with the snow traction. That said, next winter I will get winter tires. (It was too late in the season this year - I just got the car recently.)
I just talked to someone whose 2004 Prius was totalled by sliding in the snow this past winter. Needless to say, she definitely recommends snow tires. I got mine the middle of March and only drove through one snow storm, but it handled fine. I will get snow tires this fall however--don't want to be in the same boat as this woman. She ended up with a Civic hybrid, since she had no car and couldn't wait 12 months for a new Prius.
3 winters in Minnesota with a 2001 Prius. 1 winter in Minnesota with a 2004 Prius. Not a lick of trouble all 4 years from either of them, and that's without snow tires.