Greek writers set Greeks apart from other peoples, who were referred to as barbaroi, i.e. speakers of "bar bar" languages -- that is to say: not Greeks. We see this in Herodotus, who specifically sets out to immortalize the deeds of both Greeks and "barbarians". But this notion is arguably older: in the Homeric Iliad, composed ca. 700 BC or a little later, the Greeks (referred to as Achaeans, Argives, or Danaans) are distinguished from the Trojans and their allies in a number of ways, most notably language. These allies, incidentally, include the Thracians. (Diomedes and Odysseus steal a chariot belonging to the Thracian king in the tenth book of the Iliad.)

It goes a bit too far to delve too deeply into ancient ethnicity, but suffice to say that this is a complicated topic. Certainly, a "rival region" set specifically against a monolithic "Hellenic culture" is something desperately in need of nuance. It presupposes that all Thracians conceived of themselves as a single people and that they deliberately sought to compete, somehow, with people who identified themselves as Greeks. Examples of this are limited: one that pops into my mind is people from the island of Paros, including the warrior-poet Archilochus, seeking to settle the island of Thasos while meeting resistance from people identified by the Greeks as Thracians.

Indeed, in the case of Archilochus, he specifically refers to the Saians in one fragment. The Saians are a Thracian "tribe" – again, such terminology is a difficult subject, but let's roll with it for now. Archilochus has been forced to abandon his shield because a fight didn't go in his favour. He writes (fr. 5 West; transl. West):

Some Saian sports my splendid shield:
I had to leave it in a wood,
but saved my skin. Well, I don’t care—
I’ll get another just as good.

The term "warrior tribe" is so generic as to be meaningless. Virtually any people of the ancient world can/cannot be described in this way. It suggests that the Thracians were somehow more warlike than other peoples, but such subjective descriptors are usually less than helpful. It's not as if the ancient Greeks were markedly more peaceful, after all. (Again, this is a complicated issue, and research suggests that warfare wasn't nearly as endemic in ancient Greece as its cultural significance might suggest. My book, Henchmen of Ares, explores the cultural aspects of warfare in greater detail; it's based on my PhD thesis, which can be read for free here.)

A lot of our information about ancient Thrace comes from archaeology, which isn't too helpful when it comes to identifying deities, and Greek authors, who clearly had their own agendas. Herodotus, for example, mentions that the Thracians worshipped only Ares, Dionysus, and Artemis, adding that their kings, however, venerated Hermes (Hdt. 5.7). Obviously, the names of these deities would have been different; it was customary for the ancient Greeks and Romans to identify foreign deities with their own.

In Greek mythology, Ares is associated with Thrace, i.e. the area along the northern edge of the Aegean basin. It is sometimes thought to have been his birthplace; the playwright Euripides even calls Ares the patron deity of Thrace. Euripides, in Alcestis, claims that Thrax ("Thracian") was a nickname for the god; other sources suggest that Thrax, in the sense of the founder of the Thracian people, was a son of Ares. (The ancient Greeks created founding figures for all ancient peoples, including themselves.)

Ares was not so much the god of war as he was the god of slaughter; his half-sister Athena is more properly a goddess of war in the sense of warcraft and strategy. To underscore his bloodthirsty nature, he is associated with "wild places", which for the ancient Greeks included Thrace. But he was also significant, if the ancient sources are to be believed, among various other peoples who lived beyond the Greek world. Again, according to Herodotus, the Scythians worshipped Ares in the form of a sword; they sacrificed animals and captives to a sword stuck into a pile of brushwood (Hdt. 4.62).

And, of course, Ares is considered the father of the Amazons, the fierce warrior-women who were believed to have their capital at Themiscyra on the River Thermodon (possibly in Anatolia). Ares was also associated with other things that underscore his "wild" nature, including dragons, the blood-thirsty Keres (demons who suck the blood of the dead on the battlefield), the lesser deities Phobos and Deimos (Rout and Fear), and so on.

In the Iliad, there is a famous passage where Zeus, Ares' father, tells his son that he hates him (Il. 5.890–891):

To me you are the most hateful of all the gods who hold Olympus. Forever quarrelling is dear to your heart, wars and battles.

Still, Ares is the son of Zeus and Hera, and it is therefore no surprise that he lives on Olympus. He might not have been the most popular of Zeus' offspring, but that does little to diminish his godhood. He may have been born in Thrace, but place of birth has little do with determining whether or not a deity is allowed on Olympus; Dionysus, the god of the vine, was also said by some ancient sources to have born in Thrace.

This reply is based in part on an article of mine about Ares that's available on Ancient World Magazine. If you want to know more about Ares from a mythological point of view, you can start by checking out what Timothy Gantz writes about Ares in his excellent book Early Greek Myth (1993, two volumes).

I hope this goes some way to answer your question.