I'm from western South Dakota years ago we had pickups and not that many were 4x4
put some weight in the back and a good snow tire will help a limited slip differential would help also. I do remember shoveling snow from my driveway into the back of my 67 chevy truck just to get to work.

 

I used to have a 2wd 5-speed and I live in CT. I bought good decent all-terrain tires which definitely helped, weight over the rear axle works wonders...until we got more than 4 inches snow. 4wd was needed, and a 4x4 was what I got.
I know it might be a hefty financial decision, but instead of spending the money on studded tires and still having lack of reliability in the snow, perhaps you should bide your time, save up some extra cash, trade in the 2wd, and upgrade to a 4wd.
That's what I did a couple years ago and never regretted that decision

 

4wd is the best option. You dont really have to worry about snow or getting stuck. My dakota was great in the snow and no amount of snow would ever stop me. Just put it in 4wd and go. I only hope my ram is as good in the snow being 9,000lb might be a good/bad thing lol