As you may have noticed from perusing our Materials page, freezer labels come in a wide variety of types, based on specific "recipes" containing the basic ingredients of substrates, inks, adhesives, and liners. Of all the freezer label ingredients, the adhesive is almost always the most important. You can't have it deadening and releasing due to either the cold or the presence of moisture. Considering all the settings in which freezer labels are used, it takes many different adhesives in several categories to cover all the bases.
Most true freezer-grade labels use hot-melt adhesives (HMAs), which are exactly what they sound like. Think of the kind of glue in a hot glue gun. We take something similar, which often comes in little pellets the size of your pinky nail, and melt it using heat before applying it to the label substrate. HMAs have substantial advantages over other adhesives: typically, you don't have to deal with solvents, drying, and curing time, and they have a long shelf life. In addition, HMAs stick to a wide variety of materials, including corrugated cardboard, and they don't shrink or lose thickness during drying, as other adhesives can. But the melting heat limits an HMA's usage with some substrates; only those that can handle the melting temperatures without deforming or degrading—such as foils, metalized synthetics, and some thick papers—can be used with this type of adhesive. They're less likely to be used with plastics, though some polypropylenes and vinyls can handle the application heat.
HMAs used for adhesive labels tend to be made of a rubber-based or rubber-like polymer with high initial "tack" (stickiness), and for standard use must be able to adhere using simple pressure, in environments ranging down to a specified minimum application temperature. Generally, they're designed to stick even on already-frozen surfaces (as low as -20° F). They must then continue to adhere in all temperature conditions down to the adhesive's lowest rated temperature—usually about -65° F (or -54° C). Many have no problem handling frost, condensation, and other moisture that may cause some adhesives to deaden or slip.
These days we mostly use artificial polymers for hot-melt base materials, including polycarbonates, polyolefins, styrenes, and silicones. However, several manufacturers have recently announced initiatives to create HMAs using natural materials called "biopolymers," for reasons of sustainability. Many artificial HMAs are made from non-renewable petroleum-based materials, so bio-based HMAs look like the wave of the future.