Frozen is the term for the solid state of matter and film is already solid so we should say stored below 32 degrees F . Many film retailers and photographers routinely refrigerate film to prolong it's life and stability. Color film tends to undergo slight color shift as it ages and some photographers have been known to plan particular shots around the color rendition that they know they will get when a certain type of film reaches a specific age. I don't know if the plastic canisters they use nowadays for 35mm seal as tightly as the old metal screw top ones that had rubber seals. I saved a bunch of those.
Film can mildew even after processing if improperly stored.
The emulsion is an organic gelatin, and as such, is susceptible to mold and mildew. Try to always store film, processed negatives and slides in dry places. Anybody can do it with money. The true art is to do it on a shoestring.