Something narrow should be your first concern for driving on icy roads. A 12.50 is way too wide to be good on icy roads. Interco makes several tires in 10.50 which is a lot better, although a 9.50 would be even better. I think they make TSLs in a 33x9.50, and BFG makes their MTs in that size. I personally like Interco tires for the climates I deal with (Reno and Alaska) because their rubber is so soft. A siped, narrow TSL is actually a pretty damn good snow tire. The TRXUS MTs are great too and a lot quieter than TSLs.
Cooper and Toyo also make MTs that are good snow tires. Depending on your location, they can either be really cheap or expensive though. The Cooper MTs are really popular back in Alaska right now because they're a good price and do well on the ice. I also ran a set of Hankook MTs as my winter tires for many years. I actually really liked those tires both on the ice and offroad. They were a lot quieter than the old BFGs and lasted just about as long. They didn't cup nearly as bad either.
The new Goodyear MTRs look like great ice tires, but I wouldn't put them in the same MT league as say a TSL or LTB. If you don't need the mud clearing as much, they're good at just about everything else. I'd say the BFG MTs would be a decent tire if they were narrow and siped. They have the potential to have just as much if not more braking traction than the old chevron pattern did. Whatever you get, for ice you will need a narrow tire, and siping will make a big difference. Siping will also make them quieter and wear a lot more evenly.
Personally I only run snow tires in Alaska where it's really bad. Cooper M/Ss and the BFG commercial tires are my favorites, and then everyone triple studs them. Down in Reno/Tahoe it never gets bad enough for me to worry about. I run 10.50 LTBs down here and they're been about as good as a tire that wide can be. I'm going to sipe them prety soon when I'm not working on my K5 all the time. The old-style Goodyear MTRs on my K5 do pretty good, although they will slide a lot since they are 12.50s and just way too wide for a 4500lb truck. The next tires on my DD in Reno will probably be Goodyears or TRXUS MTs.