Now I don't know what Winchester used for a finish but in 2010 I acquired a Parker-Hale 1200TX target rifle and like those that belong to a lot of the serious target shooters it needed a good clean on the outside. Especially where the leather shooting mitt was in contact and the pistol grip area. It was just all cruddy and built up sweat, dirt and dust ................................. yuck.
So I soaked a flannel patch in Parker-Hale 009 nitro solvent and wiped the stock down. It took several goes but it softened up the grime and lifted it off leaving the original finish in tact. I have used this method before on several guns including an antique Mauser 1893 sporting rifle by DWM. After the cleaner evaporates a wipe down with a soft clean cloth and a rub with a spot of BLO brings up the finish a treat. BLO must be used very sparingly a small drop goes a long way. That's where lots of folks go wrong they slaver on too much.