The enemies while 'stored' are principally mould, wax moth and mice.
Mould is best tackled by first getting the bees to clean out the combs. Then storing dry. Refrigeration is probably overkill. Mouldy combs look dreadful, but the bees are actually pretty skilled at cleaning them up … Warmth encourages mould, so cold storage is nevertheless good.
Wax Moths can turn your comb to dust and make a mess of the wooden frames. You can kill them (eggs, larvae, the lot) by freezing for more than 48 hours, or fumigating with Acetic Acid or sulphur candles (both of which will do the additional job of sanitising combs and boxes against many diseases). Having killed the moths that were there, you need to prevent re-infestation. You could spray the combs with a natural bacteria (sold as "Certan") providing long-term protection (and harmless to bees and humans) or try to seal them up perfectly to prevent access (I'm told wheelie-bin-liner-bags are useful there).
Mice are best dealt with by physical exclusion - such as storing the frames in a stack of boxes, well-sealed at top and bottom.
Hence some people might put the frames back on the hive for cleaning (after arguing about whether above or below is better), freeze or fumigate them, spray with Certan and store in stacks of boxes (sealed into large plastic bags) in a cold, draughty, but dry garage … but few would go the whole hog.
