Your analysis has some holes in it (I don't know about Fat Rick's). Depending on how the black hole gets to the Sun and the size of the black hole, it could act just the same as a larger star simply fling the Earth away instead of drag the Earth in like if a black hole approaches the Solar System where it would disrupt all the planet's orbits. We could be flung at any speed too, I think 67K MPH is just the minimum. The scientific mechanism is the same as hypervelocity stars which are ejected from the galaxy by encounters with black holes, only difference is a stellar-mass black hole will eject at a slower speed.
I don't know why Patrick is talking about snow or clouds, since the only thing raining down would be the liquified former atmosphere. The ice would need to be filtered since it would be contaminated with the contents of the atmosphere. But that's not really particularly challenging to do and is a fantastic source of water and oxygen if you need it, that's why people talk about mining the ice on the Moon or Mars for moon bases.
By the way, Pluto is 4.67 billion miles away from us. So it would only take us 69702 hours to reach it, or almost 8 years. We can’t dig all that deep within that short amount of time. We also have to worry about the fact that once we’re passed Pluto, any remaining oxygen will become a liquid.
For those who don’t know, it took us about 3 decades to drill down 40318ft. At this depth the temperature is around 250 Celsius degrees. Which is perfect to heat up small cities due to how much heat is going to be wasted and or used for energy.
If you had to save our civilization by drilling, you'd have a colossal budget orders of magnitude greater than that we used to make the Kola borehole. Since we can't have a "mineshaft gap" against the Russkies or whoever, that probably means the entire military budget and hundreds of thousands of soldiers assisting with the drilling, the research, etc. The technical challenge is pretty hard, but all you really need is a way to insulate a vault against the cold. Geothermal heating and if you're lucky enough to not have the Moon ejected from Earth's orbit (or crashing into the Earth), tidal heating, means the oceans won't freeze completely solid and still have life and liquid water in certain pockets (this is basically like Europa or many outer solar system moons). Your mineshaft cities will need to recycle air and water, but this can be done with plants, a small biosphere, and various scrubbers that you're running off of nuclear or geothermal energy.
In reality, your money and economy likely collapses the minute people realize what's happening and how 99.9% of people dying would be insanely optimistic and it's up to whoever has the biggest guns and most equipment to save as many people as they can.
(A, L)
