Members of the exclusive Bighorn Golf Club in Palm Desert, Calif., now have a new citadel for their show cars to dwell with the Vault at Bighorn, which opens today. The new 24,000-square-foot automotive amenity is not only an exquisite enclave for housing cherished classics, concepts, or supercars, but also an inner sanctum for socializing.

Set behind circular bank-vault doors (and guarded by a security system that includes fingerprint scanners, 360-degree HD cameras, and 4K monitors) is a pillared, museum-…