Are the trees in that area large enough to have supported a tree-house for the former kid-residents? Maybe the wire is a DIY extension for either power for a light (bad idea) or a one-way run from the home intercom to call the kids in for meals/bedtime.
Trees around here do get big enough. There isn’t one over there now, but there could have been one over there that was chopped down long ago. Considering the wire, the tree house and tree could have burned down decades ago. This can go in the possible but not probable category, I think. The house is on a lake and there are some big trees near the water. I’d expect any treehouse construction to have taken place there if anywhere. Maybe a rope swing into the water as well.
Those are definitely power cables. Time to break out the metal detector!
[Moderating]
@Bear_Nenno , it’s probably very unwise to publicly post your address like that. If you really want, I’ll put it back, but meanwhile I’ve edited that out of your post.
I have seen a few instances where homeowners will install 120 VAC lights up on big trees, perhaps 10 to 15 feet off the ground.
Any chance there ever was one of those now obsolete 6 foot satellite dish in your backyard.
I would expect that to have a co-ax cable.
Mine is coaxial with power cables for positioning the dish.
MamaPlant’s house had an electric pole light near the driveway. Someone knocked it over at New Year’s Eve, and we never replaced it. I didn’t dig up the cable.
My house had one of those when I bought it. It had two coax cables that went into the house for the tv. Not sure how it was powered.
Do this. Now.
Same with many Yagi/beam antennas on towers: coax or Twinax is used for the signal, and seperate power/control cabling goes to the rotor. However, a quick web search shows the latter consists of three to six conductors.
With just two, large-gauge conductors, it is likely it was meant to power something, probably with 120 VAC. (And, as mentioned previously, not to code.)
Sure, if you want to do it the wasy way. 
I’m not familiar with the large C-band dishes but I’ve seen cables for them that consist of two coax and two multiple-conductor cables to power the motors, all bundled together, which is nothing at all like this twin pair of heavy-gauge single conductors. For the compact direct-to-home satellite dishes that you commonly find nowadays, the only power requirement for the dish is for the LNB (the low-noise block amplifier at the focal point of the dish) and that power is supplied through the coax itself, similar to the way power is supplied to TV antenna pre-amps.
I wouldn’t rule out the possibility that it was low-voltage, and the wire gauge was just whatever was readily available and bigger than necessary.
It’s an outstanding idea. Truly.
But a quick check for the OP’s state (GA) presents one … probably minor concern:
It looks like this is organized and executed by a consortium of local utilities, each of whom – ostensibly – comes out and marks the location of their lines on the subject property.
But ISTM that a wires installed by a homeowner or by a long defunct company/utility may quite likely not get marked at all, both failing to illustrate the path of the wires and to identify the original purpose of the wires.
IOW: if nobody sent out to locate the wires is responsible for those wires, how likely is it that they’d mark them as – in effect – existing, but nobody’s property?
Anybody have any experience with the service in their own area that can speak to the (in)accuracy of my assumptions?
ETA: I think some of what I asked about is answered here:
It’s great advice. I actually called 811 weeks ago before coming across this wire. I have a lot of work getting done on this house, to include land clearing, grading, etc. There are flags and spray paint markings for the gas, water and sewer lines. But that’s it. All the power and telephone cables are above ground and come in high from the street pole. All of the underground utilities are on the North and North East portion of the property.
One thing to keep in mind about underground utilities is that some of them – notably communications cables – might be just a few inches underground even when professionally installed by the utilities themselves. I can think of two examples.
At a previous house, a neighbour’s minor landscaping managed to cut my telephone cable which was running a few inches below ground near the border between our properties.
At the current house, when fiber was run through the neighbourhood, every homeowner had the option of getting fiber run from the street up to the house at no cost. Bell guaranteed that there would be no damage to the lawn. I didn’t pay close attention to how it was done, but it appeared to be basically a device that split the sod, pushed the fiber cable down into the soil beneath it, and let the sod come together again. I’m guessing that it couldn’t have been more than a couple of inches deep.
FWIW, I have seen that exact type of twisted pair wiring running along the baseboards of a very old house. It was installed with nails that looked like long-shanked thumbtacks with thick-padded heads. These nails were hammered in between the two wires of the twisted pair, with the wide head fastening the wires to the baseboard (what we would now accomplish by straddling the pair of wires with staples or clips). The wires I had seen used this way, terminated in a 4-pin telephone socket (not modular–the kind with the big, clunky plug–four round holes in the socket). I remember seeing multiple pairs of these wires going in/coming out of these 4-pin sockets. Why your twisted pair was buried underground–instead of coming off a utility pole–I couldn’t tell you… unless no utility pole was available… or if someone rigged up a phone extension to a neighboring barn, shack, or cabin.
I can confirm, having cut my neighbour’s fiber access with my lawnmower.
Did your neighbor have a word with you about raising your cutting height? 
I called Bell immediately and told them I had cut their cable (although my service was unaffected even though it was on my lawn). They said they were sending someone out right away to fix it; no one came.
My neighbours were on vacation at the time and came back to a mysterious internet outage. So the cable got fixed a week or two later (after the neighbours complained).