Animation Coloring

I posted this in the 'Help Me' board, but it's been over a week and no one has responded, so I'm posting this here, so it's more likely to be seen.

For my next art project, I've decided to color the wingless version of this free animated icon, but I've never done anything involving animation, and I can't figure it out. My main problem right now is that whenever one of the layers is made invisible, the horse has blocks of blank white on it. I tried looking up a tutorial on coloring animation, but couldn't find anything that seemed to address it, so I could use some tips. :3
Not sure if that makes sense or not, but help would be highly appreciated!

I'd double check with the artist and make sure they allow it to be recolored first. They say the icon is free but then say don't edit it.

Usually in GIFs white spots happen on transparent layers because it doesn't handle transparency well. A picture would be more helpful as I can't see what's happening.

<sup>Gifs don't do partial transparency, which is what happens when you use a brush tool. Use the pencil/pixel tool for clean/non-white spaces on transparent bgs. 

Like Eliza said, a wip or screenshot would be more helpful to see whats going on, but that Artist also says not to edit the icon. You might want to use one of her other resources instead which are allowed to be recoloured; Crazy Jump & Canter Icon</sup>

Oh, tysm! I didn't realize it wasn't allowed to be recolored. c: