I wouldn't even let them mount a satellite dish on the house. That sits on a pad and a pole out behind the house. (You have to do that around here, else Mr. Wind will steal it. I'm just a few mountains away from Mt. Washington.)
The tradeoff you pay for the plus side of living at a higher elevation, I guess. Mr. Wind will gladly steal your ham antennas too. So it sounds like simply standing up a TV mast and attaching it to the eave of the house is not likely the way you'll want to go.
You need something sturdy, so I guess your plans are to erect a tower. But it will need to be above your house peak (unlike your satellite antenna), and the aesthetics of that still may bug you, or your wife, and maybe others. There have been many, many battles over towers, and there will be many, many more. You can get some protection from state/local restrictions by a federal preemption called PRB-1, but it does not cover everything, notably any "covenants" that you may have entered voluntarily.
See here for more info.
You should seriously investigate your local zoning regulations about towers. I know you are remote, but you could still be subject to county zoning restrictions and you may need a permit. There could be restrictions on tower height, especially if you have an airport nearby. Some folks think,
"It's better to ask for forgiveness than permission." But you don't want to pay a lot of money for professional installation, and then turn around and pay again to have it taken down. (
It happens! It looks like this old case was in the Portland, Maine area, but the link to follow it no longer works, so I don't know the resolution of it.)
I highly recommend you get informed about tower installation by those in the know for your county, not just folks like me guessing about it. Keep good documentation on the entire process... permits, engineering details and specifications, inspections... the kinds of things you might need to defend your tower in court, if it were to come to that.
Here's an example from PA of how the ham seemed to do everything right and kept their tower.
This thread is coming along nicely.
I've enjoyed it, for my part. I don't spend much time on here anymore, and especially in Off Topic. But I'm glad that you carved off this thread and gave it a life of its own. I hope I've helped a bit.
Ham radio and Linux are a good mix... both are available to anyone of varying skill levels, and both are well suited to "tinkerers" and those who like to understand how things work "under the hood." Of course Linux is free, but ham radio can be very low cost for those who make that a goal, even if it's not your personal goal.