The stump that is still there when everything else has gone
Drive any old pasture edge in this county and you will see it. Maple stumps from the same era are soft brown rings you can put a boot through. Poplar has vanished entirely. And there, still standing proud of the grass with sharp edges and a red-brown face, is a cedar stump that was cut when the current owner was a child.
Eastern red cedar is not really a cedar, it is a juniper, and its heartwood contains oils and extractives that fungi and insects will not work on. That is the same property that made it the standard fence post in Middle Tennessee for a century and the standard lining for a clothes chest. Left in the ground, a cedar stump does not rot on any schedule a landowner cares about. Waiting it out is not a strategy here the way it arguably is with a silver maple.
What that means when a wheel touches it
Cedar is not especially hard. It is fibrous, stringy and full of resin, and those three things together make it awkward rather than slow. The wood does not chip cleanly the way oak does; it tears into long strands that wrap and pack, and the resin gums the wheel and holds grit against the teeth.
The practical consequences are worth knowing before you compare quotes. The spoil from a cedar grind is bulkier and lighter than hardwood spoil and it mats into a mass that resists spreading. The smell is strong and it stays in the yard for a week, which most people enjoy. And the wheel needs clearing more often than it would on a maple of the same diameter, so a twenty-inch cedar is not the same forty minutes a twenty-inch hackberry would be. It is not a dramatic difference, but it is real and it is why cedar rarely comes in at the bottom of its band.
Cedar plus wire, which is the local special
The two Hartsville facts collide here. Cedar was the fence post of choice and cedar grows in the fenceline anyway, which means an enormous share of the cedar stumps in this county have carried wire at some point. The rot resistance makes it worse rather than better: the tree that swallowed a staple in 1970 is still standing there in perfect condition with the staple inside it, whereas a softer species would have rotted around the metal and dropped it out years ago.
So the sensible default on any cedar stump in a line is to assume metal until the flare has been checked. That check costs a few minutes with a detector and a poke around the base, and it is the difference between a routine job and a broken tooth pocket. On a lone cedar in a lawn, planted as an ornamental and never fenced, none of this applies and the grind is straightforward.
Whether to grind it at all
There is a real argument for leaving some of them, and it is worth hearing before you spend money. A cedar stump cut low, out in a field where nothing is mown close and nothing is being built, will do no harm for the rest of your life. It will not sprout, because cedar does not sucker from a cut stump the way beech or locust will. It will not attract termites into your house from fifty yards away. It will just sit there.
Grind it when it is in the way of something: a mower deck, a fence run, a drive, a building footprint, a new planting, a pasture where a hoof could catch it. Grind it when it is an obstacle at the edge of a lawn where the mower has already been damaged once. Do not grind it because somebody told you a stump in a field is untidy, because that is the least persuasive reason on the list and it is your money.
The short version
Cedar heartwood does not rot on any useful timescale, so waiting a cedar stump out is not a plan. Grinding it is fibrous, resinous work rather than hard work, it makes a bulky mat of spoil, and any cedar that stood in a fenceline should be treated as full of wire until checked. Out in a field with nothing near it, though, a low cedar stump is genuinely harmless and can be left alone.