Just some advice on tires and winter driving from someone who has seen a substantial ammount of snow driving in his life.
The best option is obviously snow tires and a narrow tread is always best since the truck weight per square inch is at its highest and you will especially notice it when turning or braking.
All Terrain tires would be second on my list for winter this is what I run year round. Once again skinny tires are best my stock size is 245/75/16 and I stick with that size and it seems to work out great. A wider size would be better in the dry esp on the highway but I prefer not to compromise my snow performance. Now as far as all terrain tread pattern this can be a difficult one. Several tire brands offer the Mountain On The Snowflake rating and this tells you the tire is supposed to do better in the snow. I say supposed to be better but I have had some tires without the snowflake rating that were fantastic. And several over the years with the snowflake rating that were just ok in the snow. Your best bet is to read many reviews to see what AT tire to try.
It is my experience that a good AT tire that has excellent rain performance usually does pretty good in the snow. Keep something in mind there are different levels of AT tires some are not that aggressive and some are border line mud tires. My sister has some Kelly Springfield AT tires that are borderline mud tires that are fantastic in deep snow but loud! On road and not much good for anything ells. So read reviews before you buy. I run Cooper AT3's and I find them great in the dry, rain, and real good in the snow are there better yes but it is a real good compromise tire that does quite well in every driving situation I have faced.
All season tires are my third choice and can be difficult to find a winner in snow. I recall once asking this guy who had some no name all season tires on a plow truck thinking he was going to say just how bad they were and he says they are fantastic in the snow! I was like wow you just never know? Again read reviews some all season tires are fantastic in many categories esp quiet on the road but are not much good for much ells. But keep in mind if you only get a little bit of snowfall per year it is really not much of an issue.
Keep safe this winter and remember even cheep tires if that is all you can afford are better then bald tires.