Ulthuan

From how I understand the rules, the Frostheart does not gain the Blessing of Asuryan ability if ridden by either Caradryan or an Anointed. Is this correct?

You are correct, for whatever reason the Annointed does not bring along his ability to dispel. You should note that Caradryan doesn't have that ability either (either mounted on the frostheart or not), only the Annointed does.

You're right. I figured maybe I'm reading some rules wrong, still very new to me! But the PG still get the battleshock buff because he has the key word "anointed" below his name. That was something I initially missed.