... okay, so not Christmas, not exactly. The Romans didn't have Christmas—or at least not until the conversion of the Empire, and even then, it's a little unclear at what point Christmas properly speaking started. But they did have an end-of-December holiday that they called Saturnalia. Saturnalia was a multi-day festival in honor of the god Saturn. We actually have a wealth of sources surrounding the holiday (though never quite as many as we'd like to have), which sounds a bit more like Mardi Gras than Christmas, involving the crowning of a kind of "Lord of Misrule," a lot of temporarily legalized gambling, and the giving of small trinkets as gifts. Oh, and there was animal sacrifice, too. (Which I guess we still have, in a sense; we just eat the animals.)
And the holiday drew a certain amount of Scrooginess from some quarters, as well. This passage from Seneca's letters to his friend Lucillus (which, I fully admit, I scavenged from Wikipedia), gives some sense of what it would have been like to be around for that particular Roman holiday. He sounds exactly like a contemporary person complaining about how Christmas starts ever earlier, resenting the shopping crowds and Christmas music, and wanting nothing so much as some peace and quiet:
It is now the month of December, when the city bustles the most. Legality is accorded to public frivolity; everything resounds with great preparations, as if there were some real difference between Saturnalia and the normal work-week. Nothing matters—to such an extent that it seems to me that the person who said, "Once it was the month of December, now it's the whole year," wasn't wrong. If you were here with me, I'd gladly ask you what you think we should do—whether we should do nothing in our usual way, or, so that no one sees us at odds with the spirit of the season, have a more festive dinner and throw off the toga. (Letters 18.1-2)**"December est mensis; cum maxime civitas sudat. Ius luxuriae publicae datum est. Ingenti apparatu sonant omnia, tamquam quicquam inter Saturnalia intersit et dies rerum agendarum. Adeo nihil interest, ut non videatur mihi errasse, qui dixit olim mensem Decembrem fuisse, nunc annum. Si te hic haberem, libenter tecum conferrem, quid existimares esse faciendum: utrum nihil ex cotidiana consuetudine movendum an, ne dissidere videremur cum publicis moribus, et hilarius cenandum et exuendam togam."