Is it better to breathe through your nose or mouth when cycling? I just watched the 'Road to Glory' documentary about Team Sky.  I noticed when they were warming up on their Turbos, some of them had cotton wool up their noses.

Is this because it's better to breathe through your mouth than nose?  If so, why don't they have cotton wool up their noses during the actual race?
Breathe however you need to in order to get oxygen in. This goes for your mouth, nose or a combination of both.

Riders warming up on their trainers have cotton in their noses that contains something like vapor rub that helps open up the nasal passages. They don't have it in their noses during the race itself.