Chemical degradation of the powder and the primer will happen no matter what condition it is stored in. It may take longer to decompose in a more controlled environment, but the process is never halted, unless you are willing to go to extremes.

Brass will go brittle over time. Copper jackets will corrode. This can be mitigated some by applying protective coatings (as with tuff cloth). I had a box of 35 remington that was pushing 30 years old and had been kept in a relative safe environment most of that time. Upon shooting it, many of the cases exhibited stress cracks, particularly where the head meets the body. After 3 or so of those failures, I uncorked what was left of the box and deactivated the primers and tossed the lot. Generally, I don't like to keep ammo beyond about 20 years under any conditions, and shouldn't have to for now.