Exceptions to a CDL include 390.3(f)(3) "The occasional transportation of personal property by individuals not for compensation nor in the furtherance of a commercial enterprise... BUT 383.3 Applicability. Paragraph (b) says the exceptions in part 390/3(f) do not apply to this part. The employers and drivers identified in 390.3(f) must comply with the requirements of this part, unless otherwise provided in this section. 383 does not have an exception for personal transport of personal items, furthermore guideance question 9 says that states can extend the CDL requirements to non commercial and recreational vehicles... When the CDL was implemented I remember being told an individual could purchase a CMV and drive it without a CLD but I cannot find anything confirming this except 390.3(f)(3)...
Florida's laws go beyond this. See F.S. 316.003(66) which defines commercial vehicles. I don't know about other states, but non-commercial use is generally not a defense in FL. So long as the minimum Federal standards are met, states are free to be more restrictive when it comes to driving requirements. And of course Florida is going to exercise this right!!
Just as 1 of the other members mentioned if you don't actually own a farm you'd still need a CDL however if you have a farm i think you can drive up to 100 mile radius without a cdl