Try a light sanding and see if that takes off enough colour, if it doesn't then there's prob not much you can do. I'm sure the chickens won't care what colour it is

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If it's wet, sit it out in the open during the day with all the doors open. If you have a windy spot even better as that will dry it quicker. Then cover it over or bring in at night to prevent frost dampening it again. Even though it's cold out and not much sun the air will still dry stuff very well.
Consider wheels or skids rather than legs, as Lord Flynn says legs are a pain in the butt. Some people find an old cart and slap the house onto that. The stack of pallets idea is very good too, I might try that myself!
Does it have a felt roof? If so, you might want to replace that as it'll be a haven for red mite.