So the ancient Greeks and ancient Romans were two very different groups of people who lives across many very different periods of time. What the archaic greeks is very, very different than the lives and behaviors of people who lived in early imperial Rome. To address the question and the variation, I'm going to address fires for cooking/warmth/etc that took place in Archaic Greece (less my area of study but I have some experience in Homeric studies) and Imperial Rome. I'm a food historian, so I can speak mostly to the question of fires used for cooking.

Archaic Greece is definitely going to have more of the ritualistic element attached to fires, but these rituals were far from daily occurrences, and instead were mostly practices associated with festivals and important events. The Iliad and Odyssey, while they were literary texts, actually give us a pretty good set of sources to use to understand animal sacrifice. While neither the Iliad or Odyssey are "histories," the cultural practices discussed within them are revealing of cultural practices from the time, and there are lots of scenes of sacrifice. Eating and cooking meat was a communal and sacrificial act known as Thysia: the animal is sacrificed, prepared, cooked, and the inedible parts of burnt as an offering for the gods. The "savour" of the meat is sent up to the gods. This is one of the cornerstone greek religious practices. In addition to the literary evidence we have for ritualized animal cooking and consumption (they're called form scenes for a reason! they are nearly identical in content and describe the process of feasting almost identically), we also have archeological evidence at religious sites and sanctuaries. The only animals that would've been sacrificed were domesticated animals. Hunted animals, fish, etc would've similarly been hunted and consumed but largely were not the objects of such cooking rituals. There is less literary evidence from the period about these eating practices, but certainly lots of archeological evidence of the bones of wild boars, deers, etc, at expected cooking sites.

Animal sacrifice certainly didn't die out in Imperial Rome, and animal sacrifice remained an important communal ritual that involved fires. The process is pretty similar: domesticated animals were slaughtered, their offerings were burnt, the meat was prepared and served at the banquet, but often the prepared meat would've only served the priests and esteemed guests, while others fend for themselves.

If there is some argument to be made that in Archaic Greece, any consumption of a slaughtered domesticated animal invoked some religious significance (hence why fish, which were not religiously significant, were so popular), this was not even remotely the case in imperial Rome, where the rich could eat basically whatever they wanted. Roman satirists like Petronius, Juvenal, and Horace provide ample examples (hyperbolic but still instructive) of the larger than life banquets the upper class enjoyed. Eating still held a communal element, but the food was prepared by slaves, and there was no real religious or ritual component.

There were also other "communal" systems surrounding fires in imperial urban Rome, as most of the poor did not have their own ovens, so dough was brought to communal ovens/public bakeries. This is not a campfire per se (it is certainly much farther from campfire than the archaic greek example) but is indicative of a communal culture of food production and consumption, because fires or ovens were not common in the small, poorly ventilated apartments known as insulae.

I don't know anything about decorative logs or fires, but I hope this sheds some light on the ritual and religious significance that could be associated with the consumption and cooking/burning of certain animals, and how that meaning shifted over time. I'd argue that the consumption and cooking of food almost always invoked some kind of communal significance (whether you were eating in a group, at a public food counter or public bakery, or whether you were present at a religious sacrifice), but those routines and rituals do not, to the same extent, include the fire.

Some sources worth checking out are Courtesans and Fishcakes, The Black Hunter, and Ritual Meals and Votive Offerings.