My powder/bullets/primers/cases have been in unheated, un air conditioned areas for 30 plus years. Never had any powder go bad, primers either.
It can be (at the coldest) around 0F for a night or two at times. In the summer it's just ugly. Temps in the mid to high 90's. Humidity high enough that when you open the door, even at 6AM to go to work it hits you like a bucket of warm water.
My Lee dies have had rust on them a time or two (outside). The handle of the Lee press gets rust on it where I sweat on it. Never had rust on the internals of the powder measure (not yet anyway). I started putting a coat of resizing lube on the metal handle of the press and on the outside of the dies. So far, the RCBS dies have not had and issue, not sure why. The old Pacific dies have some type of hard chrome coating on them and they've never rusted either.
I store all my (well, almost all) ammo in the shed and the garage, too. When I got the GII a couple years back I opened up a case of SA surplus 7.62X51 that had been in non-climate controlled storage since 2007, so almost 10 years. No issues with any of it so far.
As they say, your mileage may vary. The internet is full of people hollering their guns rust on them in the house, let alone in an attic, garage, storage shed or the trunk of their car. I guess I'm just lucky - or I'm careful about wiping them off with an oily cloth and not touch the metal after I've wiped them down. So, I don't pay much attention to the crying about climate conditions and rust as long as it's not left in the rain or the roof doesn't leak on them.
Oh, every now and then we get some funny weather conditions down here in central VA. I've gone to the garage for something (where my reloading stuff and a couple cars are kept) and the humidity and temperature are just right (or wrong) and the moisture is beaded up on the cars, the tool boxes, the metal cabinets, etc. Weird. It's only happened a couple times in the 6 years or so I've had the garage, but it happens.