And a lot of those foods were temperate-climate plants.
Not stuff that might grow at the sub-zero temps it would take to freeze a mammoth whole.
If you had an animal that big, and you decided to freeze it on purpose, we’re talking about 20F-30F degrees below zero for an extended period. Perhaps up to a week or so.
Certainly not overnight or in 2 or 3 days...
One speculation is sudden massive pole-shift of the Earth on it's rotational axis.(physical shift, not magnetic). Think of the Earth as a spinning, precessing top in space. For whatever reason, perhaps a near-miss by a passing asteroid, e.g., it's rotational axis is altered and regions formerly temperate are suddenly shifted much farther "North" in a matter of only a few hours.
Such a cataclysmic movement would probably also result in massive wind storms (hundred's of MPH) as the Earth's atmosphere "slides around" to catch up with the land movement. For the new northern regions these winds might also contribute to rapid, "freeze-dry" type cooling.
Lot's of stuff on the net and in books about cataclysmic earth changes, e.g. Velikovsky, and others.