redeye, I don't know how common it is to put ammo on ice but it works for me on those hot 100+ degree days. It's also not like cooling down beer or cokes.:
I just take a small cooler with about 4 inches of ice in the bottom. My plastic ammo boxes just sit on top of the ice not down in it.
I have done quite a bit of temperature testing and it is quite surprising (or at least it was to me) how much temperature effects your ammo. Some powders are more stable than others but I can tell you for sure if you do your load development on a nice 65 or 70 degree spring day, then go shoot those same rounds after they sat around on your bench for an hour in 100 degree heat........ they will be "hotter". (pun intended)