We wouldn't freeze to death here. Starve to death maybe. If I remember Carl Sagan's Parade article correctly, the detonation of only 1% of the world's nuclear stockpile (1980's stockpile, mainly an exchange between the then USSR and the USA) would result in a nuclear winter.
But to answer the OPs original question, we didn't do anything. We are already "prepped" against most types of disasters. The only type that isn't really worth preparing for is nuclear annihilation. That being said, when the alert came in I made the following assumptions:
1) It was most likely a mistake. These types of mistakes have happened dozens of times before.
2) If it wasn't a mistake, the missiles were probably from North Korea, and despite their claims, none of their ICBMs have survived re-entry.
3) We have no reason to believe their missiles have any accuracy.
4) It is HIGHLY unlikely they would be targeting the Big Island.
Based on those assumptions:
1) If the attack was real, in a worst case scenario, we might have to deal with fallout from a distant location. We have time.
2) Our daughter lives in Honolulu and called us immediately after the alert wondering what to do, and she was crying. It was most important to talk her through this rather than make any preparations here. I had already provided her with IOSAT potassium iodide tablets with the instructions not to take them unless somebody who knew what they were talking about told her to, or if she was positive it was not a "threat" but an actual fallout situation was occurring or imminent. And we reminded her not to take them yet. She started to seal off her windows and doorway like we had previously discussed.
In a fallout situation, it is safer to shelter in a place with poor shielding than it is to exit such a facility and travel to a place with better shielding if it means exposing yourself to fallout to get there.
If you don't have somewhere to go without windows, close the windows you do have, shut the doors, and shelter in your hallway. You can tape off the hallway entrance with a tarp and duct tape. Tape off the gaps under the doors, or block them with towels/clothes etc.
In a fallout situation you aren't trying to protect yourself from exposure to radiation that occurs near the blast site, you are trying to protect yourself from exposure to particles (dust etc) that have become radioactive and have traveled from near the blast site. Fortunately these particles aren't radioactive for very long, which is why they tell you to shelter in place for 10-14 days. You want to avoid any contact with these fallout particles and the best way to do that is avoid going outside, and avoid allowing any outside air in. If you've already been exposed, the best thing you can do is to wash them off (take a shower, and scrub really good), assuming you can do so without exposing yourself further. If you are contaminated, you will spread that contamination to others especially in a confined location.
Unless you are at or near the blast zone (unlikely considering the current threat), going into lava tube is probably a bad idea. The goal isn't to protect yourself from blast radiation, it is to protect yourself from radioactive particles that may have traveled short or long distances to your location. If HNL was hit, the radiation from the blast site can only reach us by traveling on these particles.
ETA: Links to IOSAT tablets. They are good to have on hand especially when you know you will probably never need them. Don't take them casually, but they may help prevent the most common type of cancer that comes from exposure to radiation or radioactive particles (fallout):
https://www.amazon.com/IOSAT-Potassium-Iodide-Tablets-Count/dp/B01ALA3334/ref=as_li_ss_tl?ie=UTF8&qid=1515951401&sr=8-3&keywords=iosat&linkCode=ll1&tag=pw016-20&linkId=00039e646ee020f264ff2d522bf622cb
https://www.amazon.com/IOSAT-Pack-3-Iosat/dp/B01LMPIR06/ref=as_li_ss_tl?s=hpc&ie=UTF8&qid=1515951591&sr=1-1&keywords=iosat&linkCode=ll1&tag=pw016-20&linkId=8cc804a55e4e5c067d97fa56b20becf6
