The big cold weather warning I have always received was not oil or grease outside the bolt: it was oil or grease inside the bolt slowing down the firing pin and firing pin spring in cold weather.
I also learned the hard way that with my son's Remington Model 700 muzzleloading rifle, after a season of black powder matches 20 shots per match, seven matches per season, he started getting misfires requiring a second strike. When disassembled, the bolt (which had simply been removed and cleaned externally after every match*) was internally packed with a sludge of powder residue, oil and cleaning products. Cleaning the bolt internally after every match, leaving a light coat of oil on the striker and spring, fixed the problem of light strikes. I presume if we had gone hunting that fall, the sludge would have gelled up solid in the cold.
*Disassembling a Model 700 bolt to get to the spring/firing pin or a Model 700 ML bolt tp get to the spring/cap striker can be intmidating; requires use of a metal cabinet edge and a dime.