Well I have also pulled in the snow, but unexpected and while I had chains for the TV and 5er, I also had a 4x4 TV. It was coming home from the Oregon Coast on Hwy 26, snowing heavily, snow starting to stick on the flat, but once started the first climb the road was covered. I made it about 1/3 of the way up that first climb in 2 wheel, when I felt the rear start to break loose, I reached down and put the 2001 Ram in 4x4 and trucked on.
Held speed at about 45, I also used braking action of EB carefully. We got stopped on an upgrade as a OSP officer had traffic stopped for a spun out car, no issues getting moving once cleared.
In my opinion your biggest issue is that you only have 2 wheel drive.
This is where the the 4x4 insurance policy comes in. If you need to stop, it is easier to get started and moving again, and the big one is you have far more control with the front wheels driving. When turning a 4x2 will tend to push, especially with a locker rear-end.
The one thing that 4x4 doesn't give you is the ablity to drive the speed limit, you still need to drive for the conditions!!!
One last thing is KEEP YOUR DISTANCE.