Two words.
Dog sled.
Alright, I try and give a decent answer.
This is what you do. Wait for the first good blizzard and go downtown to the coffee shop and look at the pickups sitting out front.
Somewhere in that row of pickups is one or two that wont have snow packed around the wheel-wells, grill and mud and grass hanging out of the bumper.
A couple of them wont have a front bumper that curls up on the ends like a smile or look like someone has tried to tear the bumper off with a chain and a tractor.
Some of them just won't have a front bumper.
Look for a pickup without those tell-tale signs and what ever tires it has, buy those.
I will tell you what I look for in a tire for snow, mud and ice on a prepared surface (i.e. an actual road).
Tall and skinny with good sized lugs that clean well. Not a big fan of big floatie tires.
Don't get me wrong, big fat tires look really cool on a nice pickup, but they have a ton of rolling resistance and wont get down and dig as well as a narrower tire.
Traction is a function of psi. More weight per unit of area will yield more traction, period. This is assuming of course that there is a bottom to dig to. If you get into a batch of that west-river gumbo that is good and wet, you might as well get your personal affects out of the vehicle and start walking. More than likely your truck will be gone by morning having sunk away during the night.
Good luck.