I think the lift depends on the water content (and temperature) of the snow.
We had a lot of 'Dry' snow this past winter. Six or eight inches of snow that
could be quickly cleared away with a snow shovel. Pretty amazing.
If it was under 6", I didn't even use my back-brace!
One problem was trying to walk around in the deep dry snow..
Snow shoes would just sink 3 or 4 feet to the ground..
When I fell backwards, I made a hole in the snow. Hard to escape from!
Sitting on the ground, on the back ends of the snow shoes, snow well over my head..
And nothing to grab onto, to pull myself up..
I think driving over 8 or 10 inches of super dry snow wouldn't be a real problem.
The chains would help with those wide tires (toboggan effect tires)..
I wouldn't try anything over 6" with the Prius, unless it was blow-away light stuff.
When I used to drive the old Laser RS, it's wide tires were pretty useless in snow.
A set of smaller rims and 4 GoodYear F42 snowtires solved that problem..