It depends a lot on the conditions. Snow and ice conditions vary over a great range. Fresh snow up to a few inches can be ridden with pretty much any tire. Deeper than that and you might do ok with a 4" or wider tire. I don't have a fat bike so I'm not too sure. Deep slush is immpassable as far as I have seen. Partially packed "mashed potatoe" snow is really hard with 2" tires but can be done with 4" tires. Nicely packed snow can be ridden with anything. Ice requires studded tires