Yes, they do look animé-ish, and the Japanese seiyuu for Frozen (or Anna to Yuki no Jou, as the local version is called) are brilliant.
Anna to Yuki no Jou was actually a mega blockbuster seller in Japan, more popular there than even in the US. :3
Go watch and pretend that it's a new production from Sunrise, Toei, or CLAMP.
Hey, you never know re: Fate. Shoot me the details, and I'll be happy to accommodate. Also, you can always create new characters. Controlling the Master and the Servant? Why, hello!