St. Moritz sits high in the Swiss Alps' Engadin valley, and yes, travel insurance is worth carrying here even though Switzerland itself is about as safe and well organized as travel gets - the honest reason is the terrain, not the country. Winter sports are the whole point of a St. Moritz trip, and skiing, ski jumping at the Olympia bobsled run, or off-piste touring above the resort carry real injury risk that a routine city policy sometimes treats as an add-on rather than a given.
Switzerland's mountain rescue system is fast and effective, but it operates on a direct-billing basis that can run to a significant sum if you are not properly covered, particularly for a helicopter lift off a piste or backcountry slope. Confirm your policy names winter sports and mountain or helicopter rescue specifically rather than assuming a general medical benefit extends to an Alpine evacuation, since this is where an uninsured skier can face a genuinely large bill regardless of how minor the injury turns out to be.
For anything beyond what the resort clinic in St. Moritz can handle, expect a transfer to Chur, the regional hospital city for the canton of Graubunden, with more complex cases moving on to Zurich, Switzerland's largest medical center, a few hours further by road or rail. Confirm your policy covers transport between Swiss facilities as well as the initial treatment itself.
Winter, roughly December through March, is when the real activity risk concentrates, though summer hiking above the resort carries its own altitude and weather exposure worth checking against your policy's terms. Keep any clinic paperwork, resort or rescue-service incident reports, and receipts for treatment or equipment loss, since claims involving mountain rescue tend to need more documentation than a routine illness. Check whether your existing health cover extends abroad and specifically to Switzerland before assuming it applies, and confirm winter-sports and rescue cover are named outright rather than left to interpretation.