If lowering the temperature is the only change in conditions, then you would not expect a protein to denature. However, proper protein folding depends on many factors besides temperature. Salinity (salt concentration) and pH changes can denature proteins. So you could denature a protein at low temperatures by making the solution more acidic or more basic than the protein can tolerate. You could increase or decrease the salt concentration, or the concentration of other solutes like glucose. You could also change the the composition of the solution. In other words, rather than change the amount of salt, you could change the identity of the salt. Calcium might have a different effect from magnesium, for example. The environment inside of a cell is heavily regulated and generally not subject to significant changes. Many proteins only assume their native (properly folded and active) conformation within a narrow range of conditions specific to the type of cell they are found in and the role that they play.
