You want a narrow tire for winter traction, you want to slice through the snow and not ride on top of it.
Pick a smaller tire and you will save some money and have better tire options for winter.
Go to a 285/45/22, it's .7in shorter and almost an inch more narrow. You can get the Toyo Observe G3 Ice tire for like $210 a piece if they are still available through Discount tire. The Conti Viking Contact are little over $300 a piece in that size. The Cooper snow tires are $270 a piece, plus they have a $50 rebate on a set.
Otherwise they have plenty of other non winter tires in that size that are good all season tires. The Toyo Celsius or the Toyo Aklimate, the AT3W is nearly $100 less than the AT4W. There are other brands too but the Hankooks aren't what I suggest for people anymore, sure they are good tire but they're better tires with better tread designs that handle the winter better.
Any decent winter tire will dominate any of those all seasons though. It's a night and day difference, once you run them you'll never want to go back to a regular 4 season truck tire for the winter.