Seriously, if you have an original Winchester 1873, you probably don't NEED a gunsmith, as the gun was designed to be repaired in the field by somebody with a knife blade and a precision rock.
Find a proper YouTube video showing an ORIGINAL gun being disassembled, not a Uberti or other replica, and you'll know about as much about the gun as most modern gunsmiths would.
If the gun worked when you put it away, then there's probably nothing broken. The firing pin is all one piece, and extends the length of the bolt; There is no firing pin spring, only a pin-to-bolt 'retractor' tab that also serves to keep the two together as they move. Such being the case, you may find that that long firing pin is frozen in place by rust and/or congealed oil and grease. You can check by simply pushing on the rearmost end of the firing pin to see if it moves freely and that the forward tip of the pin protrudes from the bolt face. If it does not move, then you have either a 'philth' issue, or previous damage to the firing-pin retractor tab that has finally decided to call it quits and is now holding the pin locked in place. If it moves but the tip does not protrude, then you have a broken firing pin. It's most likely, though, that your gun simply needs a soak and a bath. That should always be 'Step 1'.
Disassemble it, or just remove the butt and forearm wood, soak it in ATF and acetone, and see if that resolves the issue.