I wanted to make a dude that sells war dogs that look like pomeranians & poodles. The only problem is that I can't seem to figure out how to edit the dog skin. I tried looking at the creation kit wiki, but it doesn't mention anything about editing skins. Is there any possible way to do this?

You can't create or edit meshes and textures in the CK. You would need 3rd party programs and then afterwards you would import them in.

What kind of program would I need to download to do that?

For meshes: Blender, Maya, 3DS Max, etc.
Blender is the only free one, but you can get the other two free as well if you are a student somewhere.

For texturing: Photoshop, Gimp, Mudbox, etc.
Gimp is the only one that's free, but again, I believe you can get the rest by having a student email. Maybe not Photoshop.

You only need one of each. I've been using Maya and I'm liking it so far. They're all going to have fairly steep learning curves if you've never done anything like this before. I can't comment on texturing since I've never actually tried doing it yet.

Photoshop has a full-featured 30 day free trial.

A Pomeranian named Pom-Pom?

I'm pretty sure a dog is its own race, so you'd have to make more races and give each one a unique skin or seriously edit the dog skin so you can change their color, hair and whatnot.

while you're at it, shrink the dang collision box for dogs so you can get around the little boogers.