First, I don't know. But from what I've seen making the generic dilution bases for pigs, I would not recommend storing the carts much below whatever HP says is their temperature range. Somewhere they probably have that number. The co-solvents in inks (not the pigments) are dissolved in the solution. At some point, if the ink becomes too cold, you may push some of these out of solution and get precipitation or separation.
In general, of course, chemical reactions are slower at lower temperatures. With at least some pigments, the coating that gives the electrostatic repulsion to the particles slowly oxidizes, compromising the dispersion of the pigs.