AT3's are not dedicated snow tires, but they're very good all season tires... If they have more than 50% tread, they should be more than adequate.
While I agree that lifting the truck isn't going to help much, if you haven't adjusted the torsion bars for the weight of the plow, it probably should be done, and will pick the front up out of the snow if it's sagged down some due to age and the plow... (Is your truck pretty nose low even with the plow on the ground?)
To adjust front ride height, park the truck where it's good and level, and drop the plow with the blade straight. Now take a tape measure and measure the height of the quadrant at the plow, and then back where it pins to the truck. (The quadrant is what connects to the truck on one end and the plow on the other.)
I suggest setting the ride height so the truck end of the quadrant is about 1/2" higher than the plow end. That seems to work well to keep the blade from tripping easily, and to let it rest fully on the ground when angled. It also maximizes ride height with the plow lifted. Don't be afraid that adjusting the bars well give a "stiff" ride... That's only if you crank them several inches, and the stiff ride comes from having no droop travel. Adjusting the ride height with the bars doesn't change the spring rate AT ALL. (Trust me, I'm a chassis engineer...)
You can go a
little higher if you like, but keep the quadrant no more than 1" out of level front to back or it'll trip too easily. (Because the truck ends up pushing down on it instead of forward, and down helps trip the blade...)
4-5 turns of both bolts gains you 1" in ride height, and that's what I add for plows on both 1/2 ton and 3/4 tons. Be sure to turn both bolts an equal amount of turns, and since you live in WI, use copious amounts of schmoolie on the bolts a day or two before you want to make adjustments. Jack the front of the truck up too, so there's less tension on the bars before you try to turn the bolts... Be warned, one of the bolts usually sticks out quite a bit more than the other. DO NOT make them the same. Just turn each bolt the same number of turns.
The snow looks pretty wet in those pictures... Wet snow will get you stuck more easily, but there are several things you can do to help yourself.
Use reasonable tire pressure. I set the fronts at door sticker pressure most of the time. If the truck only plows your drive, or does only infrequent short trips, drop them to 45psi. The rears should be run at not more than 45psi for an empty bed. From there, add 5psi for every 500lbs of cargo you carry. If you're running 70psi in all four tires, they're not able to deform any, and traction suffers greatly. If you never leave your drive, you can easily run the rears at 35psi, and you'll have much improved traction. If you refuse to heed this advice, don't bother reading further, because you're already setting yourself up to fail, and it won't make much difference...
DON'T SPIN!! If the snow is wet, and you spin, it's ice. That fast. If you have really aggressive tires, and there's non-frozen dirt under the snow, spinning might help get down to the dirt, but on previously plowed driveways with some packed snow and ice, spinning just gets you stuck in a hurry.
Use momentum. Don't drive into deep snow, stop, drop the plow, and then try to go. Drop the plow while you're moving. And if you're making a run for the road, don't stop right in the snow the county plow leaves... That crap is really stiff. Blast through. I used to make these runs in reverse, so I was set to drop the plow and head back into the driveway immediately, since I lived on a busy road. That seemed to help a lot and left less snow in the road than driving out forward.
If you find the back of the truck sliding around, put some weight at the tailgate. Start with 500lbs. It makes a HUGE difference. I cut a board to fit the slot in the bed just behind the wheel wells, then toss sandbags or whatever behind the board. That keeps them in place pretty well. Oh I see you have weight... Plenty...
Finally, if you're still having issues, get a set of chains for the front. You'll probably have to stick with cable chains on a Silverado, since there isn't much clearance even with 245's, but they'll make a huge difference if the going gets wet or deep.
Hope you find some pointers that are helpful, and not too remedial.
BTW, I do live in NM at the moment, but I spent a LOT of time plowing in Houghton MI (UP) while I was in college, and helping my dad set up his trucks to plow in Northern Michigan. I still have a snow plow for my Jeep, and I'm looking forward to getting some use of it once we've moved to our property in Colorado next winter!!
Chris
(Whew, sorry for the book... That was a lot of info to lay out, and I tend to use too many words... )