Only if the gun will be kept in the unheated garage, or out in the car/truck. You don't want to take a warm barrel from the house into the cold, and have moisture condense inside the barrel.
Be sure to clean and dry the barrel of oil from storage. Use alcohol to dissolve the oil and grease, so it can be poured out of the barrel. Now dry the barrel with a cleaning patch.
Then put a very THIN coat of oil on a cleaning patch, and run it down the barrel to lightly oil the barrel. That prevents rust, but is not so much as to foul your powder charge. I stop a few inches above the breech plug, so there is a bare area where the powder charge sits, in the back of the barrel, and where the PRB will be seated. I like to grease the bore with a greased cleaning patch AFTER seating the ball, to protect the barrel from rusting during the night and hunt the next day.
Put good tape over the muzzle to keep snow out of the barrel. The Air in front of the PRB will blow the tape off the muzzle before the Ball reaches the muzzle. ( Don't block your front sight with that tape.) I put a toothpick in my TH so that no moisture can get into the barrel to my powder charge. I usually remove the toothpick, and save it in a pocket in my pouch.
Consider soaking a cleaning patch in alcohol( I carry a small bottle of alcohol in my pouch when hunting in below 32 Degrees F. weather) and placing in half in the pan, and the other half covering the TH and leaning up over the barrel. Then close the frizzen to hold the cleaning patch against the Th. The evaporation of the alcohol will draw any moisture that has gotten into the powder charge, out through the TH. You may have to renew the alcohol in the patch every couple of hours, but its not a big deal.
Keep that lock up under your arm, and you should have no problem with snow getting into the lock. You generally will have time to prime the pan when you hear a deer or see a deer heading your way. In snow, deer tend to move slowly unless they are scared by someone or pushed. The air is so dry their sense of smell is not as effective, so they tend to move slowly stopping often to listen, and look, to compensate for their diminished sense of smell. That gives hunters the time to prime their locks.
Or, of course, you can do as others have suggested, and I have done on days with better weather, I prime my pan, and check it every half hour. If its beginning to crust, I change the prime. I use to use only 4Fg powder for my prime, but lately, I have begun to prime with whatever is down the barrel, and eliminate carrying an extra horn. Both 3Fg and 2Fg powders ignite fast enough that it makes little practical difference in a hunting scenario. :thumbsup: