My experience with the intake restrictor plate is with the Cessna 185, and for that airplane, operated at very cold temps, that plate is designed to prevent overboosting the engine, based on density altitude of induction air. That engine (IO-520) will make well more than its rated 300 hp at -30 to -40 F. The 185 has an alternate air door, which I'm not sure the 180 has, but maybe. The alternate air door, located in the induction tunnel of the cowl, opens inward (from the inside of the cowling) in the the induction filter is iced up. Iced up filter causes a vacuum in the induction tunnel, which opens the alternate air door to allow warmed air from the lower cowl into the induction. If ice is the issue, you just go home with unfiltered but warm induction air.
If, on the other hand, it's -40 (and, btw, you do know the ONLY good thing about minus 40, right?? You don't have to convert F to C) and you put the restrictor plate on to warm the induction air. The restrictor, when you push up a lot of power, such as on takeoff, creates a vacuum in the induction tunnel because the inlet hole is too small for full power. Again, that opens the "backfire door", allowing warm engine compartment air to flow into the induction, thus increasing induction temps, and preventing overboost.
The rest of that Cessna "Cold Weather Kit" consists of the plate that goes over the right side of the main cooling air inlet (to the right of the prop). It has two slots, one to allow some air to flow over the oil cooler, the other limits inlet air to the interior heat system. Again, this is on the 185, can't speak for the 180.. There's also a similar shaped plate that covers the left side of the cowl inlet.
But, what those plates effectively do is severely reduce cabin heat air flow, and block a LOT of cooling air from flowing over the engine. In the 185, with those plates installed, surface temps at -30F, engine was fine till you climbed out of the inversion (and there's always an inversion in Interior AK when temps are that cold. Climb up out of the inversion to say -25F and you'll watch your CHTs spike really fast. So, back down in the inversion....and slog along in extremely cold temps all day......really dumb.
What everyone operating in really cold temps with the fuel injected Cessnas anyway, is put duct tape over about half of the oil cooler, install in the induction plate, and go fly. It makes no sense to block off cooling air to those cylinders. Close the cowl flaps in the climb if need be.
But, that induction restrictor will prevent overboosting the engine at takeoff power when it's -30 or colder, and I've done a lot of those.
Is the induction plate really necessary on the 180?? Nope, just use carb heat if your induction gets iced over, or if you are taking off in extreme cold and concerned about overboost. Carb heat is your friend.
And, I would NEVER install those block off plates on the engine cooling openings. I knew guys who worked out of NARL (Naval Arctic Research Lab) in Cessna 180s. A couple of our 180s were assigned there, and had been to the North Pole more than once. Those pilots told me they never installed the cooling air block off plates, just duct tape on the oil cooler.