A bike is not more dangerous than a horse. You ought to wear a helmet on both (this coming from someone who doesn't yet wear the new mandatory approved helmets for showjumping.. I will probably get one next month--I'm not riding right now anyway).
At least on a horse, you usually don't fall on pavement. But I've taken a nasty spill on soft sand (the horse fell down too), and had quite the concussion. Get a riding helmet TOO.





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