There appears to be some confusion regarding the example I posted. I put character/creature on there to show that you can do a character AND a creature if you wanted. Such as a Nazgul riding a Fellbeast for example. If you're just doing a character, just put "character."

Examples of creatures would be:

Wargs
Fellbeasts
Oliphants(sp)
Hourns
Dragons
Ogres
Trolls
Goblins
Orcs
etc.

Ringwraiths/Nazgul would be considered a character, as there are specified number/name for them. In the Nazgul's case, only 9 of them. Same for other named "creatures" like Gollum. If they are specifically named, consider them characters.

EDIT: As mentioned below, although horses are named occasionally in the story, unless they are more than a normal horse (a unicorn or a winged horse or something... both of which are not in LotR as far as I know), treat them as creatures. Same goes for other "pets."