Not an issue. Reference my previous post where you asked about the same question.
I wouldn't even buy snow tires. Just sipe the ones you got.
You're not driving the Iditarod, just I90 or whites pass. It's ok.
Improve handling by airing down the tires as much as you can. Ina dually I'd be around 20-25psi rears for empty bed driving in snow. Also the more weight you can add the the rear, the better. But with 4wd if it's slick, the fronts are doing most of the traction pulling with the ballast of the engine and cab over the wheels anyway.
Again, not a concern in the least, imo.