Although I cycle very little now-a-days, when I used to, I never gave a thought to which watch was on my wrist. Mind you, as virtually all my watches are divers or pilots, they're pretty tough anyhow.
I have cycled (MTB) on frozen rivers, around towns and cities, up/down mountains, as well as down ski slopes (taking care to avoid skiers, but not so much snowboarders :) ) where coming off was always guaranteed! But I never damaged any watch .. although, myself yes. Downside was as I was always clipped into my bike (an Orange Clockwork), it used to stay with me whenever I did, happily bashing some part of my anatomy, as I slid downwards.