You can put a caravan on your land as long as your land is zoned for it and any regulations allow for it.
You would have to check directly with your local zoning and county or municipality on whether or not they allow caravans on land where you're at.
Some places allow caravans on your land without any restrictions and other places put restrictions on the land use and may restrict caravans or only allow them to be parked and not lived in.
You can also live in a static caravan on private land as long as the zoning ordinances and regulations allow for static caravans.
Even though the land is your own private land some places have restrictions on the land that restrict what you can place on the land so you have to check with your county to ensure that there's no restrictions.
Or if you live in a city or town they may have some regulations on what you can and can't live in on your land.
If you're out in the woods somewhere then it will likely not be an issue with you living in the static caravan on your private land.
You also do need a permit to put a mobile home on your property in some locations although in other locations you may be able to put the mobile home on your property without needing permits.
It can depend on the town, county, zoning etc.
If you live in a county that doesn't require permits, then you can often place a mobile home on your property without permits.
You cannot put a mobile home on just any land.
When deciding on a mobile home you have to ensure that the land you want to put the mobile home on is zoned for residential use and the land has no deed restrictions that restrict mobile homes.
You also have to ensure that the mobile home also meets zoning regulations and all local building codes.
Some lands have private covenants or even deed restrictions which can be placed on the property.
For example if you buy land in an HOA they will not allow mobile homes unless it's a mobile home HOA community.
The land for mobile homes must be zoned for mobile homes to be able to put a mobile home on the land.
In some places the land may not have any restrictions and you can place the mobile homes on these lands but you have to make sure they allow mobile homes.
If you buy land that is way out in the woods then you can likely easily put a mobile home on that type of land.
And in some places that restrict mobile homes you can often live temporarily in the mobile home or RV while actively building a site built home.