I have a Corolla, which should be somewhat similar to your Prius in driving ability.
I have to respectfully disagree here, a Corolla is not at all similar to a Prius for winter driving, they are very different. The difference is the Corolla has the engine in the front, over the drive wheels, and the Prius has most of the weight in the back due to the batteries, reducing the traction to the drive wheels.
I definitely agree on the snow tires though. I have run many sets, and thought I ran some good ones until I tried the Bridgestone Blizzak WS-60's, they are amazing. They perform amazingly on glare ice and snow, and even
deep snow is
not a problem as seen in the pictures. I have had the front bumper, on many occasions, pushing snow in front of the car and you can see where the lower engine pan was scraping the snow in the last pic.
Back to the Prius. The state of Maine has some of them for use (9 years with no problems!) and despite having the same tires (WS-60), they do not do nearly as well due to the aforementioned weight distribution. The other issue with them is the starting torque to get the vehicle moving, which is higher than most vehicles due to the hybrid system. The two combined make for rather interesting winter driving when compared to most front wheel drive vehicles. I am not trying to bash the Prius, just stating fact. The driver also plays into the equation, but I assume you're a great driver and know how to drive in wintry conditions.
In addition to the great snow tires, I also carry some traction mats I can put under the tires, a metal military e-tool (shovel), some sand, tow strap, and tools.
I love my VW, no doubt about it, but it does not compare to my Isuzu Trooper, which is 4WD. However, if it's so bad I have to take the Trooper, I have to question whether I should be driving 150 miles to go hiking anyway.