I have a house for sale with a Hot Tub room attached to the Master Bedroom. If you are interested in something like that, please contact me directly. I'm sure you would not have asked this question if you didn't think it was important.
But you didn't make it clear whether you were looking at a specific house that had a Hot Tub, or if you were looking FOR a house with a Hot Tub. In any case, if you are working with me as your Realtor, I would always negotiate the sale so that the Hot Tub is included in the price. We would specify that in the contract, and you can also have it inspected so that you know it works before you buy the house. (Unless, of course, you are buying the house "as is", and then it would be up to you to fix it as needed after taking possession.)
I'm wondering if you are currently talking to a Realtor, because that agent should have been able to answer your question for you. If you are buying a house from a FSBO, you are already in more hot water than the Hot Tub could ever provide! So, please, call a Realtor to represent you, and you won't have to ask generic questions like this on an internet website.
As a general rule, anything that is attached to the property is considered to be "real property" in Texas. But if it is not attached, it is "personal property." Here's an example: a refrigerator is personal property because it is not attached to the wall; but a dishwasher is part of the house, because it is installed in the cabinet and permanently attached to the plumbing. Your question was about an item that could go either way, and so none of us can answer that on here, because we haven't seen the way the Hot Tub is installed at the house you are talking about.
Enjoy your Hot Tub!
ULTRA Real Estate Services