There is a rather vague "exception" in US Federal regulations.
A shotgun with a barrel less than 18(?) inches is generally illegal.
A gun that has rifling in the bore (which can include a "shotgun" intended only to shoot slugs, in some cases) may be a "pistol" rather than a shotgun (sort of) so it may be legal.
At least that seems to be the argument being used by one fairly well-known US manufacturer. So far as I've seen, they're using this "out" only for .410 bore guns.
It's possible there could be some other reason why a particular gun might qualify for exclusion from the more general usual limitations.
But how does this pertain to snow tires? It would seem rear traction was inadiquate and a driver has gone off to the next road?