Typically what I have seen are mixed... at a local fort near me (Fort#4), alot is replicas but they have a lot of original preserved... some of it is protected in cases and some like the spinning wheel are restored and in use...
They had things behind glass that I would assume would be real. But the other items laying around loose would seem too delicate and important to risk theft or damage from elements and wild life. So I believe you're right.