Greetings from SC!

[Catherine]

Libby, your signature was not showing  so I clicked on edit for your post. I didn't do anything. I just saved the post and there was your signature as good as new. Problem solved, but I don't know why.

I have known dogs that lived with cats who acted like cats. Inter species connections are funny.
I think your bird is going to make sure the dogs respect  boundaries before any level of relationship is possible. I don't know if they can ever be friends.  
Some cats and dogs find reptiles interesting. I could picture your dogs wanting to play with them or just plain being interested in watching them. Dogs don't have a fear of snakes because they are not predator prey to each other. Snakes don't fear dogs. 
I think your bird would react to snakes, but maybe not. Has she even seen your snakes.

I keep my canaries and budgie as far from my corn snakes as possible because corn snakes eat birds in the wild and I don't want them even knowing there are birds around.

Dogs and cats don't have a natural relationship because they are both hunters in their own niches. They have different hunting styles so they wouldn't connect, but I suspect they would eat each others leftovers if there were any. 

That was a funny link by the way. 
Anything to do with cats is funny, that's why they rule the internet.