Couple of things not raised so far.
Low temperature is not a problem for BP storage, but high temperature is. IIRC, the Mad Monk said that the sulfur will start to mobilize at something like 130F, and eventually will start reacting with the potassium nitrate.
There have been discussions of powder/ammo storage and safety on various lists and fora, and a point has been raised in some of these by a volunteer firefighter and by other emergency personnel (that I cannot recall specifically - some may have been firefighters, too). After an ordinary house fire, the contents of a freezer are generally intact, and often still frozen. They recommended using an old steel-bodied chest freezer for a magazine - many of them even have a lock built in.
Normal ammunition cooking off in a fire is a low-grade hazard - the case is usually moving faster than the "projectile", and neither has much penetration. Without the confinement of a chamber & barrel, even sealed & crimped military ball can't build up much pressure before the bullet releases.
To make it personal, I don't have a spare freezer, or a place to put one, so my modern ammo is secured in a store-room and my horns, flasks, etc. are with the rest of my shooting gear, but my "spare" powder is bagged with desiccant, and stored in a corner of our freezer, next to the remaining venison. When I need a can, I try to remember to get it out so that it has time to warm up to room temperature before I take it out of the bag.
Regards,
Joel