I’m getting too old for much winter camping. But, cold weather camping is a bit of an art when it comes to fuel usage. Pressure drops off with the temperature. It does this pretty continuously, so there is no real sweet spot on the dial you can use. You have to get used to the sound it makes, and the visual height of the flame.
With “toppers” (stoves that simply screw on the top of a canister,) it starts being a noticeable drop off at around 45F or so. Some a bit before that some after that, depending on the size of the lines, valve opening & delicacy of adjustment, jet opening, fuel type/blend, wind, etc. By the time it gets down to around 25F it will usually light, then stay lit on a slow flame and eventually die off…basically unusable. Between 25F and 45F is where things get a little interesting. Sometimes it works (with a new canister, or a warmed up one,) and sometimes people have a hard time keeping anything lit. They often resort to warming one canister over the flame from another, then switching canisters to start warming up water, then placing the can in a warm water bath. Usually they work, sort-of anyway, if the water is around 34F but the topper/canister combination is not the best in winter. That includes the JetBoil. Mine starts dropping off from about 1:30 for half a liter to around 4-5 minutes.
In comes the inverted stoves. They work with only marginal pressure to feed the liquid fuel to an expansion chamber, often a tube in the flame. However, these do require a minimum pressure to run. The Caffin Stove just uses a Heat Shunt to do the same job of warming up the gas before burning it but this is prone to largish fireballs, similar to, but smaller than white gas, till the valve assembly is warmed up.
Pure butane (n-butane or normal butane) and even isobutane still fails in cold weather. Some propane is needed to keep these pressurized. (A topper also uses up the propane preferentially leaving about the last 25% in the can with only traces of propane left and unusable in cold weather.) An inverted canister maintains a pretty even gas mixture down to about -30F or so. But they get increasingly difficult to maintain much below 0F.
I used to use white gas. At -10F it would always burn. But the stoves that run WG are notoriously heavy. The fuel, however, is much lighter than a standard canister fuel. It usually contains about 20,000BTU as opposed to 21,000BTU for mixed canister gas. But the can weighs about 1/3-1/2 again the weight of the fuel. Typically, a well tuned stove of either is roughly equivalent at extracting heat values from your fuel. Yes, you loose about a half to a full teaspoon for priming a WG stove. But, in winter, you will be typically making about 4-5 liters per day(including coffee/tea/cocoa) plus meals. You will be using around 2-3oz per day for melting snow (it takes a lot more heat to melt snow than to boil liquid water, roughly, about as much heat to melt 0F snow to 40F as to bring 40F water to boiling.) Or you would use about a half or more of a 4oz canister per day. If you are out for week with your partner, it just don’t matter. You will save the weight of all the empty canisters but carry the extra weight of a heavier stove. It evens out, roughly speaking.
Personally, I would go with a reliable WG stove for cool and cold weather. Reserve the JetBoil for >40F. The copper strip down to the can can be made to work, but again, it relies on a fairly full canister, not a half full one, to work reliably. Without even a starting flame, it won’t ever warm the strip or the gas to even work. You end up using a couple canisters, as I explained above. Cold starts and maintaining enough flame to warm the stove up…this is the basic problem. Even the Caffin Stove requires about one minute. The strip add-ons likely require more. Unless, of course, you LIKE fiddling around and sleeping with your canisters.