I am sure that it would be brought indoors.As soon as they build a hangar to hold it.
There’s a hangar for the retired (and never designed to actually fly except in the test glide mode) shuttle Enterprise at the Udvar-Hazy Nat’l Aerospace museum annex right by Dulles Airport here in the D.C. area.
That place is magnifique, and it’s still only half-full.