forbid her anything and it became her desire

I would say that “Forbid her anything“ in this context is an unusual use of the imperative construction. The verb “forbid” is in the plain form, which has multiple uses: as the bare infinitive, the so-called “present subjunctive”, the present indicative non-third-person-singular, and the imperative.

A paper that I think is relevant: Imperatives under coordination, Ezra Keshet and David Medeiros. Keshet and Medeiros discuss this construction, but actually seem to conclude that it is not an imperative because of its reference to a past situation. However, I’m not sure what it is in that case.

Martin is writing a conditional sentence; he is not speaking of something that has actually happened, but is a possibility. If the sentence was written with more words it would be:

"[If you] forbid her anything, [then] it became her heart's desire."

Martin is using forbid as a present tense conditional verb because the sentence is conditional, but it is still a very likely possibility.

Here is an article about conditional verbs and their proper tense