Sanad, you are asking about camping in temperatures down to 0 F.
Personally, when I am camping in that temperature or lower, I really need at least a couple of cups of hot liquids in the morning. Also, sometimes water bottles are half-frozen, so you might need to pour boiling water in there as well. My personal rule for winter is to get at least a quart of liquid consumed before I head out on the ski trail.
I think a small alcohol stove is great for solo water boiling in summer, but not in winter. I suspect that you will shift over to a much hotter stove like your Snowpeak.
In normal operation, the butane vapor is in the top of the canister, and when you open the valve, it gets to the burner. But when it gets very cold, the butane does not vaporize, so liquid butane just sits in the bottom of the canister. For normal cold operation, that is not good. However, if you invert the canister, the liquid butane can flow out of the inverted bottom (the top) to the burner. For some stoves, this inversion is very difficult. For other stoves, there is a special stand to help it out. Some people just manage to invert the canister without stands. But in each case, I think these are remote canisters where there is a foot of flexible fuel line running over to the burner.
Now, you ought to be able to use your Caldera Cone with alcohol, and keeping the alcohol bottle in your pocket for warmth will help it along, but that may or may not get great results. You'll have to test.