Yes, magnets will damage even a floppy! Just make sure that your equipment used to store will not come in contact with magnets.
However, here is a suggestion I am surprised nobody has made: Invest in a digital wallet! iOmega and Minds@Work make some handy, light and small units which are nothing more than portable hard drives. If you can't get to saving your images on a CD, simply empty your memory card on the digital wallet. They are so light that you can even bring them along to the parks and download while taking a break, eating, whatever... No need to bring along a laptop, just a digital wallet that even fits in your camera bag.
I have the most affordable version that Minds at Work sold a year ago, and it will hold over 2,000 pictures! I bought mine on ebay and back then paid about $150.00. Don't buy directly through their website or local distributors though, at least back then the prices were higher. Find distributors on ebay. I am sure the prices have gone down. It is great because you can empty your card again and again, no need to invest in an expensive card or even several. It only takes seconds to empty your card on to the portable HD.
So if you are concerned about losing your images and don't have the opportunity to save them elsewhere, you may consider investing in one of these gadgets for peace of mind and convenience.