More trail will be a benefit in the snow, at the expense of dirt handling, IMHO.
I'd say opt for the 2.0 if you can swing the extra cost. In my experience, a 1x9 set up with a 33 tooth ring isn't low enough for the snow. In fact, I'd get the 2.0 and promptly swap the 28/38 rings for a pair that's smaller.
My fear with the 1.0 would be that the cranks don't have tabs for a granny ring and you're looking at upgrading the cranks as soon as you get it out on snow.