p-e lighters are more vulnerable to spark failure due to dust and debris than to cold. I agree that sub-freezing temperatures may cause problems for butane (not fluid zippo) lighters, but you can generally warm the lighter. However, altitude has caused me more trouble with butane than temperature... and I couldn't always "go lower".
... this may be more Lighter-lore than you want to hear, but if you want to increase your chances of the butane lighter working at altitude you have to bleed out air from the tank and then fill the lighter at roughly the same altitude where it is expected to operate...(roughly the same). This reduces (but doesn't guarantee against) the "vapor lock" or sputtering that we see with many butane lighters.