Im a pilot... (not for an airline) but as far as carrying a bike with you on a plane you'd be fine. As long as you pack it right, the only things you would have to worry about is other luggage getting piled on top of it which you may be able to avoid by telling them what it is and asking about how to label it. And heating. I can't see a reason why a bike wouldn't be alright at seriously cold temps but some pilots don't turn on the cargo heat because there's no need to. (often times when you ship pets they come out frozen if you don't remind the right people)
But those would be the only 2 things to worry about.