horseman vs animal fancier

horseman and animal fancier both are nouns.

Word	Noun	Adjective	Verb	Adverb
horseman	Yes	No	No	No
animal fancier	Yes	No	No	No

As nouns, animal fancier is a hypernym of horseman; that is, animal fancier is a word with a broader meaning than horseman:

horseman (noun)	animal fancier (noun)
a person who breeds and cares for horses	a person who owns, shows, judges, or breeds animals
a man skilled in equitation