I'm a huge fan of Michelins. I have installed 3 sets on 3 separate vehicles and couldn't be happier. They wear VERY well, run quiet, tough as nails.
I'm sorry, I can't speak to how well they do in snow/ice as we don't have that down here. But I put some on my Ram 2500 which I used off-road and for towing/hauling a lot and they did great. I have a set on my Jeep Grand Cherokee now, and they've done just fine for the little bit of off-roading I've done since I've owned it. Put a set on DW's old X-Terra, and they were great there as well.
DW just got a Tahoe that has GY Wranglers on it; they're kind of loud (can't really hear them at HW speed though which is a testament to GM's noise-cancelling tech). My Wrangler also wears the GY Wranglers, and those tires are loud, but it's a YJ, so that doesn't really matter, it's all part of the "experience"! I was thinking when the time comes to put new shoes on the Tahoe, I would put BFG A/T KO2s on there, but perhaps not after what you said...
ETA: It was the Michelin LTX A/T2 I put on my Ram 2500 that I loved so much.
-2018 Greyhawk 29MV
-2015 Jeep Grand Cherokee Limited (Primary Toad)
-1994 Jeep Wrangler YJ (Secondary Toad)
-2014 Jay Flight 28BHBE & Ram 2500 6.4L CC 4x4 (sold)