When I owned property in Grafton, NH there was a significant property tax. There is no zoning, but I can’t imagine they got rid of the property tax. Most of it pays for public schools.
(NH Dept. of Revenue Administration) Property Taxes
2016 Total Tax Rate (per $1,000 of value) $26.1
So a property valued at $100,000 would have a $2,610 tax bill in 2016.