Well, I must confess to having been left behind, at this point in time (but not at this moment in time - a truly redundant phrase unless in the context of moments of inertia - of which I have far too many.)

To me, "snoot" means nose, derivative of "snout." [c.f the Concorde aeroplane, which was described as being "droop-snoot" on account of its ability to lower its nose when landing, so the pilot can see where he's going.]

To be "snooty" is a reference to "having one's nose in the air" to describe the upper classes - presumably (although I've never checked) because of the stratagems adopted by upper-class people to avoid the stench of "the great unwashed." (Itself a stratagem to avoid the plaque, etc.)

P.S. Isn't a snood something you wear on your head?