If it’s outside city limits you are fine. If inside City of Houston then mobile homes are restricted to MHP’s or grandfathered properties, even though the city has no formal zoning. To have an MHP you must have a license in accordance with City Ordinances, Chapter 29 specifically.
You might check to see how the County has this property classified. If it’s MHP you should work with the City to confirm that they agree this is a grandfathered property and you’re okay to continue that usage - and as part of that updating the older “mobile homes” (e.g. RV’s) with newer models. Don’t get optimistic about them being eager to help.