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If you have one that goes on the outside of your helmet do they blow down, do they just channel cold air to the back of your head and can you still use a helmet light?
IME they just don't work. OthersVMV
Can't really comment on stay up factor - the hood on my Montane jacket stays up over my helmet, but it's designed to do that on top of an Alp.
Helmet lights... they use the body of the lamp as a heatsink, and the heat has to go somewhere or the lamp overheats and shuts down. If the hood is very good at keeping the wind out, it's probably going to not work too well with your lamp.
Just wear a buff or something under your helmet? A mountain biking helmet normally covers a bit more round the back of your head anyway