I'd look carefully and talk to a lender about the tinyhouse. Typically these are built on a trailer chassis and can be moved, which gets you around zoning issues (so long as they stay registered as a trailer).
But you would have a hard time getting a conventional mortgage on it, since it is technically a trailer. Ask a banker or a broker what the minimum requirements for a conventional mortgage would be. Probably 1200 sq. feet, 2 BD 2 BA I'd guess.
$65k is a big chunk of change for a tiny house, are you going to pay someone to build it for you?
Even the most ornate tiny house is only $30k in materials, most are much less.
$65k would get you a nicely done prefab from studio shed (
http://www.studio-shed.com/), on a concrete slab foundation. If you shoot for the minimum requirements for a conventional loan, you might be able to swing a construction loan that would let you buy the land, and build what you want.
Other option would be to buy the raw land, and then build the tiny house on your own time. Problem is the mortgage rate on raw land will be higher than what you might get with a construction or conventional loan.