Horse1,
Yah the all terrain with a three peak snowflake rating is the way to go, value wise. One set of tires for all season here in Alaska.

BFG AT, Goodyear Duratrac and Falken AT3W all have it. Of those three, the Duratracs are the best in mud. Falken are ok, but mine are made in Taiwan.

BFG AT ko2, though good on ice and snow, are terrible in the mud. With front and rear differential lockers engaged on an 80 series landcruiser, they still sucked on my muddy road that has no state service. Could barely get out even with lockers in spring.