Pigs don't get completely invisible

When I throwed a splash potion of invisibility on a saddled pig, the saddle didn't become invisible

What I expected to happen was...:
The pig and the saddle become invisible

What actually happened was...:
The saddle wasn't invisible

Steps to Reproduce:
1. Spawn a pig
2. Put a saddle on it
3. Throw a splash potion of invisibility on it
4. Wonder why the saddle didn't become invisible