From the link on IOWA laws;
quote
Commercial vehicle – any self-propelled or towed motor vehicle used on a
highway to transport passengers or property when:
A. In interstate commerce is defined as:
 A single vehicle having a gross vehicle weight rating or gross vehicle
weight (GVW) more than 10,000 pounds.
 A combination vehicle having a combined weight rating or gross
combined weight more than 10,000 pounds.
 Designed or used to transport more than eight passengers (including
the driver) for compensation.
 Designed or used to transport more than 15 passengers (including
the driver) and is not used to transport passengers for compensation.
 Used in transporting hazardous materials in a quantity requiring
placards.
B. In intrastate commerce is defined as:
 A single vehicle having a gross vehicle weight rating or gross vehicle
weight more than 10,000 pounds.
 A combination vehicle having a combined weight rating or cross
combined weight more than 26,000 pounds.
 A combination vehicle with a power unit gross vehicle weight rating or
gross vehicle weight more than 10,000 pound regardless of the trailer
rating or weight.
 Designed or used to transport more than eight passengers (including
the driver) for compensation.
 Designed or used to transport more than 15 passengers (including the
driver) and is not used to transport passengers for compensation.
 Used in transporting hazardous materials in a quantity requiring
placards.
QUOTE
You will note that they define "commercial" by weight -- most states do that. Farm plates will generally get you out of the biggest part of the tickets, but they are looking.
On the CDL requirement;
QUOTE
A commercial driver’s license (CDL) is required for anyone driving any of the
following sizes or types of vehicles.
 A single vehicle with a gross vehicle weight rating (GVWR) of more than
26,000 pounds.
 A combination vehicle with a gross combined weight rating (GCWR) of
more than 26,000 pounds [b:6d94253fba]when the towed vehicle GVWR is more than
10,000 pounds.[/b:6d94253fba]
 A passenger vehicle having a seating capacity for 16 or more persons,
including the driver.
 A vehicle transporting hazardous material in a quantity requiring a placard.
QUOTE
I added the bold. Your trailer is over 10k and your combined load is very likely over 26k.
There is a FARM exemption
QUote
Commercial driver’s license (CDL) exemptions
Farmers and farm helpers
Drivers of commercial motor vehicles under the control of the farmer and used
in their farm operation may claim an exception from the requirement to have a
CDL, provided all of the following conditions are met.
• Must stay within a 150 air-mile radius of the home farm.
• Must transport supplies, equipment, or products for that farm operation.
• Must transport from farm site to farm site, or to and from the home farm.
• May not transport for-hire, but may exchange services with other farmers.
Generally, drivers of farm operated commercial motor vehicles may operate
across state lines within a 150 air-mile radius of the home farm, provided the
neighboring state recognizes the CDL exception from the state of issuance. It is
advisable to consult with the officials of a neighboring state before crossing a
state line.
QUOTE
It is actually fairly clear.
(^ yeah, that was a joke!
)