To begin, a few assumptions. By 'mile wide', I am assuming you mean a mile deep, or thick, from top to bottom.
I am also assuming that the temperature never gets more than a few degrees above freezing, so no 'snow melt' days. The existinng snow is relatively permanent.
You do not clarify, but it is perhaps evident that there is an atmosphere around the planet, that 'buffers' meteor impacts. This is not a 'pock-marked planet like the moon.
You state an assumption about techtonic plates, but fail to mention if these plates move around and collide sufficiently to form mountain ranges. You mention volcanoes, however. So the question is open, if this planet has high mountain ranges. With no mountain ranges, there are no avelanches, and more importantly nothing to block the winds. I suspect the surface would be like the Arabian desert, only with blowing snow, not sand. Actually, probably like Antarctica. A constantly changing landscape, with huge drifts forming and decaying, ever changing.
Methinks also that these residents would have to be able to mine extensively, as it seems mining is the only way to obtain any sort of raw material. Perhaps they live in these mines?
And. lastly, about the most abundant material you have for building is snow, and perhaps fish and animal bones and animal hides, apart from anything they can mine.
Given these assumptions, it would seem to me that your biggest problem with earthquakes would be liquefaction of the snow. Shaking snow back and forth rapidly would cause melting, and this melting would turn the snow into slush, or even water. Think: massive flooding and sinking, a great leveling of the landscape. The hills and valleys of the snow drifts canceling each other out. In such a scenario, boats or completely floating structures would be the preferable habitat. Buildings that could be moved or towed elsewhere.
Then again, speaking of the Antarctic,
That sense of improvisation continued for decades. In 1956, the Royal
Society founded Halley Research Station, but the facility was covered
in snow by 1961 and was shut down in 1968. A replacement, Halley II,
was reinforced with steel supports, but its life span was even
shorter, from 1967 to 1973. Halley III lasted for 11 years, Halley IV
for nine, and Halley V for nearly 15, with each rebuilding effort
presenting a costly and operationally complex undertaking.
When, in 2005, Halley needed rebuilding again, the British Antarctic
Survey, which operates the U.K.’s Antarctic footprint, took a novel
approach. Hoping to avoid yet another quick-succession project, Survey
teamed up with the Royal Institute of British Architects to sponsor a
design competition. The winner, Hugh Broughton Architects, designed
Halley VI to last at least 20 years.
In addition to being visually striking, Halley VI provides researchers
with a more spacious and comfortable living and work environment. It
is set on hydraulic stilts, allowing operators to lift it up out of
accumulating snow drifts. And if the entire station needs to be moved
— it sits on a drifting ice shelf — skis at the base of those stilts
make that possible.
“Before, these projects were all just about keeping the weather out,”
Mr. Broughton said. “Engineers would be told, ‘This is the weather,
this is the wind speed, these are the restrictions.’ But now these
projects are about using architecture as a means of improving both
well-being and operational efficiency.”
The stilts-on-skis technique would also be the perfect solution to earthquakes, provided the skis could 'float' (pontoon skis).
However, these buildings were certainly NOT made from indigenous materials.