I have spent the past hour or so researching this and this is what I have found.
As defined in 49 CFR 390.5, a "covered farm vehicle" (CFV):
Travels in the State in which the vehicle is registered or in another State,
Is operated by an owner or operator of a farm or ranch, or by a family member or employee of the owner or operator
Transports agricultural commodities, livestock, machinery or supplies to or from a farm or ranch
Has a license plate or some other means specified by the State that identifies it as a farm vehicle
Is not used in for-hire motor carrier operations (but for-hire operations do not include use of a vehicle owned and operated by a tenant farmer to transport the landlord's portion of the crops under a crop-share agreement)
[From § 390.39] Is not transporting hazardous materials that require placarding, and either of the following:
Has a GVW or GVWR (whichever is greater) of 26,001 or less, in which case the CFV exemptions in § 390.39 apply anywhere in the United States
Has a GVW or GVWR (whichever is greater) of more than 26,001 pounds and travels within the State where it is registered or, if traveling out of the State where it is registered, stays within a 150 air miles of the owner or operator's farm or ranch
It should be noted that, based on my review, that even if you are a CFV your are not exempted from the DOT number requirement if your gross weight is 10,001 lbs or greater that operates across state lines (interstate),this varies from state to state.You are exempted, as a CFV from the CDL, Medical Card and ELD requirements and several others like the mandatory 30 minute break if you have livestock or live bees on board.
I know very little about this... so take it for what it is worth.