Snow tires - 2 or 4

Never bothered with snow tires growing up and living in Michigan. Modern tires are pretty darn good.

That said, if you are going to get them, of course do all 4. Tires provide the forward thrust from the rear wheels but also steering the front wheels and braking on all 4 wheels.

Check the local junk yard for cheap rims.

I would do all 4. I know just doing the drive wheels makes sense, but doing the steering wheels (or rear wheels on a FWD car) really makes a huge difference. My dad drives his '99 Camaro Super Sport year-round and puts Blizzaks on all 4 corners in the winter. It's crazy where that thing will go. I had 4 Blizzaks on my FWD Buick, too, and having all 4 definitely helps in stability. The snow tires are much more narrow and cut through the snow - best to have all 4 the same size. Tire Rack has pretty good prices on wheel/tire packages.

The tire shops recommend that if you're doing just 2, put them on the back, regardless of drive axle.

X2 on going to Tire Rack for 4 Blizzaks. They are located in South Bend, IN. I opted to have ours shipped. There might have a tax advantage for you by going that route even though you'd have to pay for shipping.

I have a 2011 Silverado 1500 2WD, and I have 2 snows. I'm not a spring chicken (in my late 60's) and grew up with rear 2WD cars. We only put snows on rear. Since the advent of FWD cars the tire guys and tire mfg's are recommending on all 4. That makes some sense, but I'll stick with my old reasons on rear 2wd! I think they have extended the 4 reasoning to sell more!

I live in the South, but raised on a farm up North. Always used 4 snow tires on dads scout and the car back in the day. All need traction to stop and of course drive. Don't have snow down here...but sugar sand... Anyway sometimes you can get those cheaper steel rims from discount tire or any tire shop and leave them snow tires on them. I don't know what stores you have up there, but here where I live I use discount tire and no issues from them. Also on ebay if you can wait that long.

Here we have to run on all 4, snow and ice rated are mandatory for driving through the higher elevations. All seasons don't cut it.
Many put snows on the driving wheels only but that is false economy, they don't steer or stop well on icy surfaces. I learned that early in my driving career.

It's a 2wd rear wheel drive, just 2 on back.

I have used just the two rear snow tires on my truck, with some sand in the back. It works fine that way.

Based on your described usage and the fact that it sounds like you can choose not to go when the conditions are not favorable, 2 on the back should be fine. We operated a good many vehicles in that format during all types of weather and conditions. Just make sure the 2 on the front are decent.

One other thing to consider with a truck of that vintage is the front brakes. If all the sliders or pins aren't free to move then you can be more prone to rear wheel spin with the front brakes dragging.