First off, unless you are experienced in stock work, do not try to refinish the stock on your Winchester 1892 unless you don't mind its value dropping like a rock. You could easily take a rifle/carbine valued at around $1000 and turn it into a rifle/carbine valued at $800 by putting a lot of time and energy into it. I see many old Winchesters with a coat of heavy spar varnish on the stocks becasue someone told someone else that the stocks were originally varnished. Yes, they were originally varnished, but with a very thin varnish that was meant to last long enough to get them out the door. If you rubbed oil into the varnish, it chips off like fairy dust. If you steel wool it, it turns into fairy dust. If you carry it and neglect it and leave it alone, it actually lasts a long time.
From doing a little searching old Winchester 1892s were oil finished. This is in reference to a Model 1892 manufactured in 1911.
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the stocks were oil finished (5-6 hand rubbed coats) with the colored stain added to the oil.
I have never heard that. I do restorations on old guns, and the old Winchester finish is hard to replicate partly because of the lack of accurate information about them, and partly due to the highly variable nature of the legendary "Winchester Red". From what I have studied, original regular production Winchester stocks were shaped, sanded, vat stained with an oil-based stain, wiped, dried, finish sanded to remove cloudiness, then varnished with a very thin hard shell varnish. They did not get hand rubbed coats, they got what was quickest and easiest, varnish. In some guns the "Winchester Red" is part of the varnish, in others it is part of the stain used to color all of the stocks to look the same regardless of the original color of the wood. I have handled several hundred original Winchesters made from the 1870s to the 1990s. I have seen custom order guns, presentation guns, and production guns. Sure, there is oil in the wood finish, they had very few other options available, but that is different from an oil finish.