I carry two different kinds of pre-lubed patches, depending on the gun I am using. For years, I have carried pre-lubed patches used with a Round Ball in my rifles, using a Brass can purchased from Tedd Cash products. I own two sizes- one the size of a percussion cap tin( which I used until someone gave me the TCP can as a present) -- and the other about 2 1/4" in diameter which I use to carry dry cleaning patches. If you go larger than .50 or.54 caliber, the smaller tin won't hold patches large enough, so you need a second larger can. When I got my fowler, for instance, which is 20 gauge, I needed a larger container to carry any pre-lubed cut patches.
Brown Bear's observation about cold fingers is correct, and you need to make adjustments in all your gear if you are hunting in cold weather. I change from using a oil/beeswax LUBE, to using alcohol to lube my patches in sub-freezing weather, for instance. Because alcohol evaporates, I carry those patches in a plastic "baggie", closed tightly to reduce available air inside during a hunt. I also carry a small bottle of alcohol in my bag, to use to "freshen" the amount of alcohol in those patches during any long hunt. Alcohol on the skin when its freezing out IS COLD, so think about how your are going to protect your skin, too.
Dutch Schoultz's Dry Lubed patches should also be considered for use in sub-freezing temperatures.
http://www.blackpowderrifleaccuracy.com/
I also carry 3" square flannel greased cleaning patches for lubing the bores of my smooth bores- 12 and 20 gauges. I currently carry them in a ziplock sandwich size bag. I carry a stack of Dry, 3" cleaning patches loose in my bag. But, if I actually cared about being HC, when hunting with these guns, I would make up a leather wallet to carry both the greased, and Dry patches.
I am going Back to cutting my patches at the muzzle, with a patch knife, and will be carrying strips of patching fabric, lubed, in a cylindrical container like those 35mm plastic film "cans" that are hard to find anymore.
So, as you have already read above, there are lots of ways to do this. The main thing is to contain greased patches- of any kind-- so that you don't get the grease all over your clothes, and hands.