I'm in the "internet forum minority" with my thinking, but I prefer wider tires in winter. (Canada)
I've ran both 10.5" and 12.5", and I only run the 12.5" now.
I cannot tell you I have scientifically backed studies to confirm that wider tires are better for traction in the snow, but it's what I think/experience.
(again, I realize I'm in the minority according to the internet on this) .
If I really thought the skinnier tire had better traction, I guess I could over-inflate my 12.5s...but honestly, I'd tend to under-inflate in bad winter conditions. Works for me.
But even if "I've been wrong this whole time", I've had nearly 30 yrs of winter driving experience...and my "wrongful thinking of wider tires are better in winter" still hasn't managed to be a negative factor yet, so it probably really doesn't matter that much with which width you go with.
Actually - now that I re-read your post and noticed you're getting mud tires...THAT (mud tires) will be the biggest negative in snow vs other treads/rubber compounds. Much more of a difference than tire width IMO. While mud tires can do well in deep snow, they often become as slippery as hockey pucks on frozen roads. Sipping is your friend in winter conditions too, which is something most mud tires are lacking in.
Technically, I guess there is more lbs/sq inch of pressure with a narrower tire...but is it enough and at the magical point where only the 10.5" tires reaches the pavement and not the 12.5? (I doubt it). Or does the extra surface area of the 12.5" make more of a difference with traction? (I think it does - but that's just an opinion).
Some ppl ride their bicycle in winter here, but primarily only with those "fat tire" wheels and not the skinny ones.
Different weight than a Jeep though, but skinny is bad on bikes in winter.
I prefer the 12.5 aesthetically. So I'm probably biased there.
But it will "handle worse" on the highway, and probably add more stress to the steering/ball joints/etc.
fyi - I run mud tires in summer, and Duratracs in winter - both 12.5" wide.
Previously ran BFG Ko2 10.5" wide - which were also fine.