Depends. (New construction?) In my state, I have heard there is a "minimum of 100sq ft" I am not sure if that is for real estate advertising purposes though, or for appraisal purposes. And, I am sure it is state-specific. (As are things like above grade square footage v total square footage.)

Code (IRC) minimum for a 'habitable' room is 70 square feet, so you are legal, assuming your local jurisdiction doesn't have stricter rules. You would have to have a big enough window to meet egress codes, and most areas don't consider a bedroom unless it has a closet.

As for realtors- my mother's old house had a 6 X 7 BR, with a closet, and it was included as a BR.

I think it depends on the rules and regs for an area too. I wanted my craft room to not be considered a bedroom, though it has a closet. The way we were able to do it was to make the bathroom on that level available only through the bedroom. If the bath were available to the whole floor, then the craft room would have been considered a bedroom too.