There are a couple of local zoning restrictions that currently prevent people from living in a tiny home. The primary issue with most zoning ordinances is the minimum square footage requirement that nearly all tiny homes do not meet.
Most zoning ordinances require the single family dwelling be between 720-1200 square feet in size. Since that is the requirement for the actual living area, it excludes attached garages, storage areas or three season covered decks. The square footage only includes actual living areas. I.E. bedrooms, living rooms, kitchen, bathrooms, etc.
Conversely, most tiny houses range in size from 160-400 square feet. As a result, they are initially considered a non-conforming structure and therefore not allowed. Because of the minimum square footage requirement, the tiny home owner will likely struggle to obtain an occupancy permit from the building inspector. If you are initially told "no", when you approach your township or county about living in a tiny house, ask them this follow up question: "What do I need to do, or what options do I have to obtain an appeal to your determination?"
As mentioned above, there are of course means at which a tiny home owner can seek to obtain approval from the municipality they would like to live within. You can always submit an application for a variance to the zoning ordinance, or also seek a special use permit for the land you would like to live on. There is no guarantee when applying for these, as the applicant typically needs to present a solid business case as to why the variance is required and what sort of hardship they would incur if they were not granted the variance.
I always recommend building a relationship or rapport with your local Zoning Administrator, as this we prove beneficial if you are attempting to gain their buy-in for the tiny house movement. Most zoning administrators are open minded, but you will likely need to present a business case with examples of where living tiny was allowed in another area. Building officials rarely like to be the first one in their area to champion this sort of change by making a precedent.
In this case, it's never a good idea to ask for forgiveness instead of asking for permission. Always be proactive in your search for an area you can place your tiny home. Being flexible in terms of where you can live will also provide you with different options, should your desire to live in a tiny house be met with opposition from your municipal leaders.