"Technically", i.e. according to how the law actually reads, as opposed to how a particular law enforcement officer or agency might choose to interpret and enforce it, there is no mention of any exception (such as private property) to the illegality of bearing a firearm outside one's home or business unless one has a currently valid CCW or open carry license granted by the police department of the county. Just like, technically, according to the way the law is actually worded, it is illegal to stop anywhere or deviate from the most direct route when traveling between any of the legal locations to and from which a firearm may be transported (e.g. can't stop to get gas or use a bathroom or into the fast food drive-through or head over to Home Depot to get a can of paint with the properly encased unloaded firearm in the car). [And they wonder why people have so little respect for their laws?!]
Now, even if they drive by you on your mower how are they going to know you are concealed carrying? And even if they did, why would they care? Unless they are investigating a roadside murder and have some articulable reasonable suspicion that would warrant a search of you.
It's pretty much they can do whatever they want... and they can be as arbitrary and capricious in their actions as they are in their interpretations of "the right to keep and bear arms shall not be infringed", wherein not one single person ("ordinary law-abiding citizen") in the entire state may lawfully bear arms outside their home or business.
But I could be completely wrong.