I think your going to have a problem with finding something good on ice - most good mud tires have large lugs that skate on ice. A few friends are running Goodyear Territory tires from CT - great for everything but ice (skating). I know guys who were travelling to mine sites etc. that used Goodyear Duratracs - they ran a dedicated set for winter with studs. That gave the best performance for winter - great for deep snow and good stopping on ice.
Goodyear Wrangler Duratracs seem to have a couple of tires that appear to be based on it's design, but cheaper price points (Territory at CT and Authority at Walmart). CT often has a buy 3, get 1 free sales on their GY Territory tires. At regular price, the LT245/75-16 Territory is pricier than the Duratrac (currently, $236/tire minus $20 rebate on the Duratracs vs. $250/tire for Territory).
From 2000-05, I ran a set of new Goodyear Wrangler AT/S (P-rated) on my Mazda pickup. They weren't very good IMO. Had to have at least two sand bags year round to keep the rear end in line. They are lowly rated by users at Tire Rack. The Duratracs are the only only GY tires that I would consider. Currently, running on a set of stock GY Wrangler RT/S....will be glad to get rid of them when they wear out.
BFG AT T/A KO are severe snow rated and are often LT load E rated....after the AT/S, I was hoping for a year round tire like the AT T/A KO would work both summer and winter. I was way wrong. I got stuck 10 times one winter. After a couple of winters with the BFG, I got a set of four studded winter tires, entry level (cheap!) Arctic Claw TXI....half the price of the BFG....got me around town a lot better. Stuck maybe 1-2 a winter (put on tire cables to get around). There is NO ONE TIRE OUT THERE!!!
An average winter gets me 8 feet of snow, very cold temps as low as -35 deg C (-40 on occasion, -50 reported in the past), ice in Jan and Feb typically.