Hmmm, I can't explain why the same batch of icing (just colored differently) would dry at different rates on the same day, under the same conditions. That is indeed odd. Usually pure egg white-based icing is very reliable in terms of its drying, as you're not dealing with possible variations in meringue powder manufacturers' use of albumen in their formulations. Is it possible you used white coloring in the icing that did not dry as well? Sometimes too much of that has seemed to delay drying for me - I think it has something to do with the titanium dioxide in it, though not at all sure.
At any rate, you can still/always accelerate drying using some of the methods explained by Terry above.