I have seen a few of them around, and I'm starting to see more. I've seen them in Georgia, and in Florida, where I'm based. With all due respect, the one that I did utilize, once, was much more significant than a hot dog stand.
The one that I utilized appeared to be fixed to a foundation. I would want to take a closer look before I opined conclusively, but from what I remembered I would consider it to be real estate. Yes, it could be moved, but remember I've seen a lot of houses moved as well, and no one is going to say they're not real estate when one is on a site.
A good rule of thumb is how the item, or structure is attached to the real estate; and a second major consideration is whether, or not, the intent was for it to be permanent. Permanent being defined as the anticipated useful life. There may be some much smaller ones than what I have seen, but the ones I have seen are much more significant, and much more significantly attached to the real estate, than a hot dog stand.
But then again, when I read "hot dog stand" I'm thinking of the ones we have around here, which are pulled behind a car or truck. You may have something different in mind.