What most 'conservatives' call small business is actually micro, mom and pop, and hobby businesses.
Speaking of corporations, some micro businesses take advantage of the far more favorable tax structure a corporation enjoys and call themselves a corporation. The ones I know are single person businesses, consultants and the like. They pay themselves as an employee, the corp picks up many costs for the 'employee'.
Many family farms are incorporated. It is quite common these days, I know one that had on it's board a 6 and 9 year old child!