I'm not a lawer, but legally I don't believe there is anything to stop you from saving an image to your PC and colouring it without asking. It's only when you come to put that work back into public domain is there an issue. I think it's polite to ask anyway, but in most cases the only way to communicate with those artists is via deviantart, which means you would need to signup on the site. So if you intend to keep the work private, I wouldn't worry about asking. If it comes a time you would like to put it on the web, or anywhere else, you could ask them then.
Also, another one I forgot about is
Colormeclub. Many artists give their work to this community for people to color. I don't believe you need to ask permission, but I believe you must credit the artist.