What is the minimum operating temperature of chemical hand warmers?
They are often made of the crystallic $\ce{CH3COONa.3H2O}$, that dissolves in its own crystal water, when heated up.

As the cooled down liquid state is supercooled solution, it is hard to predict, at what temperature it would spontaneously solidify.

It will provide heat in any case. But as it warms up itself typically by  $\pu{40-50^{\circ}C}$, it would barely warm itself to room temperature, if it was previously cooled down to e.g.  $\pu{-60^{\circ}C}$.

The air activated heaters, based on oxidation of fine metal powders (thanks @MaxW ), may have problem with too slow initial reaction when too cold. So they may need to be kept at pocket temperature for some time before activation.