What happens to a plant when it freezes?
The damage is done by ice forming in the wrong place, and the difference between a plant that survives a hard frost and one that turns to mush is mostly about where the ice forms rather than how cold it got.
The two kinds of freezing:
Extracellular ice forms in the spaces between cells. Hardy plants tolerate this: as ice forms outside, water is drawn out of the cells osmotically, so the cell contents become more concentrated and resist freezing themselves. The plant essentially dehydrates in a controlled way and rehydrates on thawing.
Intracellular ice forms inside the cells, and the crystals rupture membranes mechanically. This is fatal and irreversible — it is why a frosted courgette or dahlia collapses into blackened slime. Rapid freezing makes it far more likely, which is why a sudden hard frost does more damage than a gradual one to the same temperature.
How hardy plants protect themselves. They accumulate sugars and proteins acting as antifreeze, lowering the freezing point of cell contents and stabilising membranes; they reduce cell water content; and some produce proteins that control where ice nucleates. All of this takes time to develop — which is why hardening off and gradual autumn cooling matter, and why an unseasonal frost in May does damage a January frost would not.
Why thawing speed matters. Damage frequently occurs on rapid thaw, particularly where morning sun hits frozen foliage. Plants in an east-facing position suffer disproportionately, and shading them can help more than covering them.
Other frost damage mechanisms:
Frozen soil, where roots cannot take up water while leaves still transpire, causing evergreens to desiccate — a very common winter death misread as cold damage.
Root freezing in containers, where roots are far more exposed than in the ground and are less hardy than the top growth.
Frost heave, lifting shallow-rooted plants out of the soil.
Practical points: frost pockets collect in hollows and behind solid barriers; wet soil holds more heat than dry; and damaged growth should be left until spring, since it shelters what is beneath it.