Depends on who you ask and their philosophy on chicken keeping.
I know Ohio gets winters - I don't know how much snow your particular area gets. Is your run covered? Small bantams aren't going to venture out into snow to much, so they'd probably be inside quite a bit come Dec./Jan. If your run is covered though, that won't be as much of an issue.
Right now I do have 5 adult and three chick seramas (the smallest bantam breed - all of them combined weigh less than my one barred rock) in a coop just slightly larger than 4 x 4. We're in the process of building a new coop right now, because there's no way I'd keep them all in there for more than overnight, so it won't work this winter (hence the new coop with space).