Short answer, it's complicated. Before I get into the long answer I'll give the disclaimer that this is all my opinion, I am not a lawyer, and I am certainly not YOUR lawyer.
As I understand it a permit is not required for open carry so long as you are either on private property or outside the boundary of an incorporated city. Since the permit is not required therefore one must assume one is not required to provide one if stopped by a LEO. The details are defined in Iowa Code Chapter 724. I'd link to it but the Iowa legislature website is not conducive to static links, I'll quote a portion of the law below.
What complicates the matter further is that a LEO has the authority to assume you are hunting on the basis that you are armed.724.4 CARRYING WEAPONS.
1. Except as otherwise provided in this section, a person who
goes armed with a dangerous weapon concealed on or about the person,
or who, within the limits of any city, goes armed with a pistol or
revolver, or any loaded firearm of any kind, whether concealed or
not, or who knowingly carries or transports in a vehicle a pistol or
revolver, commits an aggravated misdemeanor.
An example, you are walking down a county road, far from any incorporated city just to take in the clean air and enjoy the scenery. You are walking with a firearm that is clearly visible on your person, slung over your shoulder or in a holster on your hip. You are openly carrying within the laws of Chapter 724 but since you possess the equipment for the taking of game a LEO may declare that you are "hunting", as defined in Chapter 481A, and may therefore demand you present a hunting license.481A.37 Presumptive evidence.
It shall be presumptive evidence of a violation of the provisions of this chapter for any person to:
1. Have in possession any fish, game, furs, birds, birdsí nests, eggs or plumage, or animals, which have been unlawfully caught, taken, or killed.
2. Be in possession of such fish, game, furs, birds, or animals at a time when or place where it shall be unlawful to take, catch, or kill the same, except game, birds or animals, during the first ten days of the closed season.
3. Have in possession any implements, devices, equipment, or means whatever of taking fish, birds, or animals protected by the Code at any place where the possession or use thereof is prohibited.
IMHO the laws are written very poorly. It is highly likely that anyone armed with anything more dangerous than a plastic coat hanger is likely in violation of either the weapons law or the hunting law.