When cold temperature is an issue, your fire may be harder to start, but you will be the biggest victim. Your cold hands and waning patience are more likely to make your fire harder to start than anything else.

Fingerless gloves are good to keep your hands warm while allowing fine manipulation of twigs and leaves, and the lighter.

You can also shelter yourself from the wind to keep yourself more comfortable as you try to start the fire. Or make yourself a hot beverage (yes, with a stove).

Also, teamwork. Take turns running around in the woods collecting fire wood (heating yourself up) and working on the fire (freezing your hands off).