Hmmmmmm 3 posts and you're attacking people who believe a responsible dog owner should have made a better call. Now don't get me wrong, I don't believe in calling anybody(especially Peta) but those conditions can cause some real issues. I've run coyotes before people knew we had them so don't paint me in the wrong camp.
I'll bet it wasn't noses bleeding, I'll bet it was ears. The edges of ears take a real pounding in cold weather, not hard to spot an eneven edge due to many days of cold running, and small raw edges can bleed a lot.
And by the way my labs are not fat so find someone else with that example.