Yes and no.
When you build a small house on a foundation, financing is pretty standard. Usually, you'll start with a construction loan to build the house, and then that loan converts into a 30 year mortgage once the house is completed. The bank may also help finance the cost of the land. Typically, they look for you to have 30% of the funds needed.
Because the house is so small, banks may have a hard time understanding that this is your primary residence and not a guest cottage. It may require talking to a few banks before finding someone who "gets it". We suggest showing them pictures from our Small House Book.
When you buy a house on a trailer from us, financing is not available. It is something we are working towards. We are redesigning our tiny house plans on wheels so that they can be classified as RV's. We are working with an architect and an engineer to make this changeover happen. Once that is done, we will do the footwork to convince at least one lender that our houses are indeed RV's. From there, financing should be available.
If you build your own portable house on a trailer financing will not be available. Technically, it isn't a house. And it can only be deemed an RV if it is built by a licensed manufacturer. Of course, if you're building it yourself, the cost of materials are low enough that you can try getting an unsecured loan such as a credit card from Home Depot or Lowe's.