Are poems reallly puzzles?

Some are if they are well written..

You can write about a person and hide it using metaphors.

The slick usage of words makes the poem like a riddle.

The key would be figuring out what the metaphors mean.

I read one good poem that described empty bottles as dead soldiers.

Not usually, no. They often pack a lot of meaning into a very small number of words, but they don't have "hidden" meanings, and the meaning isn't "behind" the poem. It's in the poem. You just have to read it and pay attention. Poets usually intend their poems to be understood, not to hide things from you.

Cross words.

They can be. Just depends on how they are written.