I once left my pre-lubed patches in my bag, on the loading bench during sub-freezing temperatures while I went into our shooting shack and got warmed again around our stove.
I probably was inside for 20-30 minutes, and when I went back out, I notices that my lubed patch( Young Country 101) was a bit more stiff than I was used to them being.
No. its wasn't frozen, or rock hard. But, I decided from then on to keep my pre-lubed patches in an inside pocket of my parka, or shirt, so that they would stay warm from my body heat. The closest I have come to knowing how the lube reacts in colder temperatures was putting a lubed patch in my freezer, and letting it stay overnight. [The freezer is rated as being at -10 degrees F., but I don't have a thermometer that goes that low to check the factory specs.] The patch and lube were still soft enough to use. So, I don't know how cold it has to get before you need worry about your patch lube. There are synthetic oils- even motor oils for your vehicles-- that are rated to work fine at very cold temperatures- and even better such oils that can be found at airports, where temperatures of hot engines, and very cold high altitude temperatures put great demands on any oil. Those oils have to work if the plane is to stay in the air.
Frankly, I don't see the need to go to that extreme, since we now have a variety of oils available to us as shooters that will handle any cold temperatures we are likely to be out hunting in.
A different issue arises about lubes and oils used to lube working parts in your gun's lock. You oil metal parts for two reasons: To prevent rusting by putting a barrier between the metal and the air; and to reduce the friction where two metal parts move against each other.
IN cold weather, I like to use very fine, synthetic oils, or vegetable oils, on the moving parts. jojoba oil, made from the Waxy bean from that plant, is a very thin vegetable oil that is considered a replacement for Sperm Whale Oil, which is no longer available since the ban on Whale hunting, and the sale of whale parts here in the USA).
When its below freezing, the relative humidity is so low that I have little worries about rust occurring, until the gun is brought in from the cold to a warm, Moist room( Kitchen,etc.) I prefer to leave my gun out in the cold in my car, or truck( or on the porch of a hunting shack), rather than take it into a warm room where condensation will be a problem both inside the bore, and inside the lock. :surrender: :thumbsup: