The website to Iowa Carry is http://www.iowacarry.ORG
Yes, open carry is legal in rural Iowa. It is also legal on private property in city limits with the property owner's permission. Even concealed carry is permitted on private property with permission.
The concealed carry restriction in a vehicle only applies if the weapon is accessible to the occupants. If cased and unloaded then there is no requirement for a permit. In my hunter education course the instructor pointed out that a firearm must be unloaded, and cased or disassembled, before being placed in or on a vehicle. He said a shotgun leaned up against a car, or a rifle placed on a truck tail gate, could get one in trouble if found loaded by a LEO.
I don't recommend testing the limits of the school grounds prohibitions but I have heard that the "gun free zone" that surrounds a school does not include private property or public through ways. The road and sidewalk in front of the school is not included in that "gun free zone" since other laws on private property rights and on unrestricted travel overrule that law. There was a case of a TV reporter being found carrying a concealed weapon on the sidewalk in front of a school. That charge of being armed while in a school zone was thrown out because he had not left the road right of way. Rulings like this one has left the 1000 foot "gun free zone" surrounding a school essentially meaningless.
I am not a lawyer and my advice is worth exactly what you paid for it.