OK, first, Zoroaster was not Persian, but belonged to some bronze age Iranian people. Second, he lived at least half a milennium before what you probably think of as "Ancient Persia", in Central Asia.

But to get more to your question: We know little to nothing of Persian intellectual tradition in the Achaemenid era. There was a clergy, which seems to have been somewhat respected for its mystical knowledge by the Greeks. On the other hand, the Greeks tended to conflate Persians with the ancient Babylonians and Assyrians who preceded them as hegemons of the Near East (hence the association with astrology).

From what we can deduce out of Late Antique Persian works, there seems to have been members of the clergy who engaged in what we would probably perceive as "philosophy". A decent example is the Counsels of Adarbad, ascribed to a 4th century cleric/vizier of the Great King:

(2) My son, think upon virtue and do not turn your thoughts to sin, for man does not live eternally and the things of the spirit are the more greatly to be desired.

(3) Put out of your mind what is past and do not fret and worry about what has not yet come to pass.

(4) Put not your trust and confidence in kings and princes.

(5) Do not do unto others what would not be good for yourself.

...

(44) So far as you possibly can, do not bore your fellow men. (45) Do not seek to be avenged on others and do not try to cause them loss.

(46) Be as generous with your property as you can.

(47) Do not deceive anyone lest you come to grief thereby.

(48) Hold your superiors in high esteem, make much of them, and listen to what they say.

...

(51) Be plain in your speech.

(52) Never speak without reflection.

Another interesting example is the Menog-i Khrad:

1. The sage asked the spirit of wisdom (2) thus: 'Wherefore is it when there are instances when a lazy, ignorant, and bad man attains to eminence and great welfare, (3) and there are instances when a worthy, wise, and good man attains to grievous misery, perplexity, and indigence?'

4. The spirit of wisdom answered (5) thus: 'As to him who is a lazy, ignorant, and bad man, when his destiny becomes a helper, that laziness of his then becomes like unto diligence, that ignorance unto knowledge, and that vileness unto a goodness. 6. And as to him who is a wise, worthy, and good man, when his destiny is an opponent, that wisdom of his then turns to stupidity and foolishness (alakih), and that worthiness to ignorance; (7) and his knowledge, skill, and worthiness become manifestly secluded.'

....

1. The sage asked the spirit of wisdom (2) thus: 'How and in what manner has Ohrmazd created these creatures and creation? 3. And how and in what manner were the archangels and the spirit of wisdom formed and created by him? 4. And how are the demons and fiends and also the remaining corrupted ones of Ahriman, the wicked, miscreated? 5. How do every good and evil happen which occur to mankind and also the remaining creatures? 6. And is it possible to alter anything which is destined, or not?'

7. The spirit of wisdom answered (8) thus: 'The creator, Ohrmazd, produced these creatures and creation, the archangels and the spirit of wisdom from that which is his own splendor, and with the blessing of unlimited time (zurvan). 9. For this reason, because unlimited time is undecaying and immortal, painless and hungerless, thirstless and undisturbed; and for ever and everlasting no one is able to seize upon it, or to make it non-predominant as regards his own affairs.

It should be borne in mind that when these were composed (orally or in writing), there was probably already at minimum a burgeoning Persian literary (as opposed to oral) tradition, that did not exist in Achaemenean times (whether they had such a tradition in e.g. Elamite, is not known). Moreover, it should also be kept in mind that Greek thought had an influence on Middle Persian literature, especially during the reign of Khusrau I Anushirvan (6th c) but also that of Shapur I (3rd c), and therefore it is hard to say how much of this represent the survival of an older tradition. However, given that the sages of Iranian peoples were in Greek times viewed with a certain degree of reverence (possibly even more in lost esoteric works), and some recurring similarities between Greek and Iranian thought, it seems likely that there existed at least a kernel of this tradition back then. It's certainly not a coincidence that the intellectual apex of Classical Greece is during its coexistence with the Achaemenid Empire.

Whether this is something you'd consider "philosophy" is up to you. I think it is worth considering that the corpus of canonical texts from Classical Greece, especially the ones you are probably immediately familiar with, is biased toward what "we" feel represent an intellectual tradition that can be traced from our times back to Ancient Greece. Clearly, however, there was an intellectual tradition in the Iran of Late Antiquity, that also extended to religious and ethical education for non-clergy, that we also see the legacy of in the flourishing of Persian intellectuals in the early Caliphate, and it is not unreasonable to think this was preceded by an earlier, similar tradition.

(Also, I clicked your profile out of curiosity, hello, fellow Swede!)