The Iowa Department of Natural Resources does, in fact, pay property taxes on some DNR owned land.

Below are property tax reports available for download.

Property Tax Reports	*.pdf
Total property taxes paid each year since Fiscal Year (FY) 2000
Property taxes paid each county since Fiscal Year (FY) 2002
Property taxes paid each county since Fiscal Year (FY) 2002 (via Habitat Stamp funding)
Property taxes paid each county since Fiscal Year (FY) 2002 (via REAP funding)