The picture Ovid gives of Tomis in his Tristia and Letters from Pontus is obviously stylized to win pity from his Roman audience. For someone like Ovid, however, Tomis probably did seem like a pretty wretched place. Take the description that begins Tristia III.10:

"If there be still any there who remembers banished Naso [Ovid]....let him know that beneath the stars which never touch the sea I am living in the midst of the barbarian world. About me are the Sauromatae, a cruel race, the Bessi, and the Getae, names how unworthy of my talent ! Yet while the warm breezes blow we are defended by the interposing Hister [Danube]; with the flood of his waters he repels wars. But when grim winter has thrust forth his squalid face, and the earth is marble-white with frost, while Boreas [the North Wind] and the snow prevent life under the Great Bear, then 'tis clear that these tribes are hard pressed by the shivering pole. The snow lies continuously, and once fallen, neither sun nor rains may melt it, for Boreas hardens and renders it eternal...." (1-14)

And so on and on. Tomis (modern Constanţa, Romania) does indeed have a much harsher climate than Rome, though not nearly as arctic as you might think from Ovid's description. Most winter days (to judge from the climatic data on the city's wikipedia page) the high temperature is actually above freezing, and the Danube only freezes solid in exceptionally cold winters. The climate may have been slightly more rigorous in Ovid's lifetime, but it was probably not qualitatively different.

Nor was Tomis as impoverished or barbaric as Ovid wants his readers to think. Although archaeological investigations been limited by the presence of the modern city, several very substantial Roman-era buildings have come to light. Perhaps the most impressive is a commercial complex known as the "Mosaic Building," which the Princeton Encyclopedia of Classical Sites describes in these terms:

"This is a huge complex of commercial buildings designed on three levels, which also served to cover and support the cliff, which is 20 m high at this point. The upper terrace, which overlooked the sea, had a mosaic floor surrounded on three sides by walls faced with polychrome marble. The mosaic covers an area of roughly 2000 sq. m..."

Although the Mosaic Building was probably constructed well after Ovid's death, there is no reason to think that Tomis was an impoverished city.

It was, however, a barbaric one to someone of Ovid's sensibilities. Although the lingua franca was Greek, the first language of most residents was probably some dialect of Getic, which Ovid was compelled to learn to speak with his neighbors. As he says in Tristia III.14:

"I have unlearned my power of speech. Thracian and Scythian tongues chatter on almost every side, and I think I could write in Getic measure..." [eventually Ovid did write a poem (unfortunately lost) in Getic)

Even those who spoke Greek did so with a pronounced Getic accent: in Tomis, Ovid laments, "Greek is mastered by the sound of Getic" (Tristia V.2, 68). The people of Tomis, in short, just weren't very similar to the smart set Ovid ran with back in Rome:
"if I look upon the men [of Tomis] they are scarce men worthy the name ; they have more of cruel savagery than wolves. They fear not laws ; right gives way to force, and justice lies conquered beneath the aggressive sword. With skins and loose breeches they keep off the evils of the cold ; their shaggy faces are protected with long locks. A few retain traces of the Greek tongue, but even this is rendered barbarous by a Getic twang. There is not a single man among these people who perchance might express in Latin any common words whatsoever." (Tristia V.7, 45-54)

This description, like the others quoted above, is certainly exaggerated for literary effect; but it strikes at the heart of Ovid's hatred of Tomis: without his patrons and his public, a Roman poet had no place in the world.