SweetBeeTreats - I think she's talking about butter seeping into her icing and spotting it; not the colors bleeding together . . . but personally, I think the two are related. I don't think I've ever experienced what others are calling butter bleed (and I wonder if it's even that; more on that in a bit). I usually mix my icings as thick as possible (so they dry faster) and quick-dry them with a dehydrator, and work in and air-conditioned environment when it's hot. I think this tactic seals/cures the icing so as to prevent both color and so-called butter bleed.
The Royal Icing Queen - I'd be cautious about refrigerating iced cookies. Sugar is hygroscopic (attracts water), so if the cookies aren't properly sealed in the fridge, the icing is likely to do weird things - including colors mottling and possibly bleeding. As far as the "butter bleed" issue, the color experts at TruColor actually think this sort of spotting is more likely the result of the cookie sucking water out of the icing at different rates (thus causing discoloration) vs. fat seeping from the cookie into the icing. They discussed this on this site somewhere recently, though having a hard time finding that post now.
At any rate, I find I get little change in color (from whatever source) if I mix and dry my icing as suggested above - similar to what SweetBeeTreats suggests, though I never mix my colors a day ahead.
There is already an extensive discussion on the site about how others handle butter bleed; check it out here: http://cookieconnection.juliau...r-seeping-into-icing