To answer the original question... Both may be encountered at that temp.
As for the most likely I suggest that it would be clear ice. You are at 0 OAT, that means the cloud above is below zero (only just); meaning the water droplets (be they small or large.... small in this case) are super cooled.
Drizzle hits AC, then freezes into clear ice. Temperature effects how far back the drops will extend on the AC due to freezing time.
For Rime to form it needs to me much colder.
BOM tends to agree.