I get some bronchial pain while huffing and puffing if it's really cold out. A scarf might help some but the better solution is to stay out of the cold. I've also found that exhaling through the nose keeps that extremity thawed. If by "sore throat" you mean getting sick later, I maintain a superstition that sickness is caused by microbes and not cold temperatures, despite evidence to the contrary.
I can't exhale through my nose most of the year. I mean the same thing I wake up with every morning because I have to sleep with my mouth open in a poorly-heated room. Whatever it's called.I've also found that exhaling through the nose keeps that extremity thawed.
If by "sore throat" you mean getting sick later, I maintain a superstition that sickness is caused by microbes and not cold temperatures, despite evidence to the contrary.