Well i don't see any harm in not peeling them if you don't mind carrots that may look discoloured and disfigured, but then saying that unless your stew is going to be filmed at close quarters for a Tv cookery program then go ahead. Personally I would peel them.
It depends. Sometimes I buy them from the supermarket (thinner skins) but mainly I buy them at the greengrocers. I'll peel them all anyway as that's what I've always done. Sometime I have the chantanelle (sp) I don't peel those as they are too small...
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