The problem with the alcohol stoves in the cold is that the stove itself has to heat up to pressurize the alcohol. So alcohol stoves will worked differently based on a number of factors.

Someone mentioned the White Box stove. It is made out of aluminum bottles, much thicker than an aluminum can. This means it takes more heat to warm the stove.

Insulation is also a factor. A cold pot resting on a stove tends to draw the heat out of the stove. Same thing happens when you put your stove on the cold ground or directly on the snow. Typically you would want an insulated base for your stove, maybe another can or cup to suspend it off of the cold ground.
To help keep the cold pot from drawing out the heat some people will carry a small piece of coat hanger shaped like a 'V' that will rest flat on the burning stove and then the pot is balanced upon the coat hanger. This keeps the cold pot from directly touching the stove and limits surface area where heat can be drawn directly from the stove.

Wick stoves do work much better with alcohol because the wick heats the alcohol closest to the wick as it absorbs it. Kind of a pre-heating through suspension as it were. It doesn't rely on the base temperature of the actual stove nearly as much.

Lastly, windscreens also play a major part with alcohol stoves. The better the windscreen the better the insulation to the pot and the hotter it will burn.

I believe the main differences are that white gas requires more moving parts and alcohol requires more know-how. But that is just my .02