Prism99

If you were living in a humid climate such as that in the deep South, I wouldn't do it but since you are in the California Hills I think you do have options. As far as I know, heat and cold would not be your problems; mice and moisture would be your big issues.

You can keep fabric safe by using hard plastic tote bins with latching handles. I have noticed that non-latching lids can warp over time, allowing mice entry; that is why I recommend the latching bins. Here is a link to the type I mean:
http://www.walmart.com/ip/Homz-15.5-...-of-4/40977738
I also recommend getting the ones with the clear plastic tops; it's surprising how much the solid tops interfere with finding stuff later on.

Never store fabric in soft plastic bags. Aside from the fact that mice can easily chew through them, soft plastic "outgasses" chemicals that damage fabrics. Hard plastic does not outgas these chemicals.

Now that the mice have been taken care of, you absolutely must address the moisture issue. If insects are not a problem in your area, you can use a drill to make small holes in the plastic to allow moisture to evaporate. Personally, I would not do this. Instead, I would use dessicant pillows inside each box to absorb moisture. These are the little packets that you often find inside shoe boxes, vitamin pill bottles, etc. Save them and recycle them into your plastic totes. You can purchase these in quantity online, and you can also make your own using the granules used to dry flowers with. Here is a link to a place where you can purchase dessicant packets:
http://www.sorbentsystems.com/smallp...FUuRHwodOR8CBA
If you want to make your own, purchase silica gel at Walmart or JoAnn's (look in the plastic flower section of JoAnn's) and watch Youtube videos. Here is a link to one Youtube video that shows how to do it yourself:
https://www.youtube.com/watch?v=ly-o7sAsFtI