How much powder and primers and how long will they be out there before you cycle through them? Primers are fairly durable and powders will last a good long time as long as they are kept in the original tightly sealed bottle. For most of us, they won't be out there more than a year or so before we use it up and replace with new stuff. They should be fine for that long even in Houston, assuming some nefarious evil-doer doesn't break into your garage and steal it before you use it up.
Ideally though, I would store it in a closet inside the house. It really doesn't take much space at all to store 15-20 lbs of powder and 10,000 primers. Just one drawer in a dresser can store that much easily. If it came down to it, I would rather have my socks out in the garage and my powder in the house. The real bulky part of storing components is the brass and bullets and they'll do fine in the garage.