Extremely hard to beat the performance of BF Goodrich A/T T/A KO2 tires. They repeatedly win Baja races. I ran them for years on my vehicles and never had problems. Not even in 8" of snow in a field. The only downside was they would break a belt about 3/4 through their useful-life (tread wear).
I went with Goodyear Wrangler Adventure with Kevlar for my current truck. My F150 is 2wdr with electronic locking rear axle. I replaced Hankook tires because I would get stuck in my backyard if the grass was wet, while hooked up to my 5th wheel. The Wranglers handled the wet grass no problem, even 2" of mud under it and pulled the 5er out without issue. I did have to lock the rear axle. Managed to test them out in one snow storm before winter subsided, no problems. As for road noise, none. They aren't cheap, but worth every penny so far.
Your best option is an All-Terrain tire, especially one rated for snow use. Look for a tire that has staggered sidewall lugs, plenty of sniping in the tread blocks to wick away water and grip snow. you want the snow int eh snipes, snow grips snow which gives you traction on snow. You also want large center channels for the water to channel away fromt eh blocks. The staggered lug and sniping reduce road noise. The kevlar adds 2 layers of toughness to the sidewall to resist rock, tree root cuts. Shop around and read the tech bulletins on each tire. Take the tire reviews with a grain of salt. Most people post to justify thier purchase.
I used to work in a service center and we sold tons of tires. the longest lasting was Michelins. Cooper tires are okay, but look better then they perform. Had a set of 33" on an S-10 Blazer for off-roading. They did great in the mud, so-so on sand/snow, and rain was iffy. But they were a mud tire, not an All-Terrain.
I was spektical of the Goodyear Wranglers, the Goodyear Trail Runners I had before didn't perform very well and had about the same ratings as the Wranglers. I have to admit the Wranglers are one of my favorites to date. I have tried a variety of tires from a variety of manufactures. The best perofrming tires was by far the BFG KO's. These Wranglers are a close second.