Freezing changes the problem twice: adhesion at application temperature and adhesion after freeze-thaw cycles. What must change in the construction for each.
Cold chain is two problems in one. At application, the surface may be cold and wet. In storage, the label survives freeze-thaw cycles that pump moisture to its edges. A construction needs different properties for each, and it is worth deciding which one you actually have.Label before freezing, at room temperature, on a dry surface: most good constructions work, because the adhesive wets out normally and then the whole bond freezes solid. Label after freezing, onto condensation: you need an adhesive designed to wet out on cold, wet surfaces — a different class. Signal of the wrong choice: labels applied in the cold room lift within the first thaw.
Each cycle moves water vapor toward the label boundary and back. Edges lift first because that is where vapor concentrates. Faces matter here: paper absorbs the vapor and swells at the edges; film stays dimensionally stable and pushes the problem to the adhesive, which a cold-rated adhesive can handle. Signal: wavy lifting that starts at the edges and grows with each cycle.
Three adjustments, in order of impact: an adhesive rated for the application temperature (not just the storage temperature); a film face for dimensional stability; and a liner and face combination that runs on cold, possibly wet surfaces in the labeling machine. Constructions selected for this are in cold chain & frozen food.
Often yes — applying at room temperature to a dry surface, then freezing, is the easy direction. The hard direction is labeling already-frozen, wet surfaces, which needs a specific adhesive class.
Freeze-thaw cycles pump water vapor to the label edge. Each cycle tests the edge seal; a construction that survives one cycle can still fail after twenty. Judge by the full storage pattern, not a single freeze.