No, they breathe fire through their mouth.
No after he gained his new body in Harry Potter and the Goblet of Fire he does not have a nose.
Well, typically smoke doesn't come out of your nose, so if smoke does come out of your nose, I suggest finding a fire extinguisher.
TRUE
Chestnuts Roasting on an open fire, Jack Frost nipping at your nose The Christmas Song (Chestnuts Roasting on an open fire)
60 Minutes - 1968 Under Fire A Dog's Nose Miracle Man 37-39 was released on: USA: 26 June 2005
Chestnuts Roasting On An Open fire, Jack Frost Nipping At Your Nose
From the song "The Christmas Song" also known as: Chestnuts Roasting on an Open Fire, it is Jack Frost nipping at your nose.
Fire ball
I believe this has to do with Pocahontas 2: Journey to a new world
heatmiser
It doesn't have to be very near the nose cone, only on the other side of the fireproof material to prevent it being burnt by retro-fire.