You see, normally, for questions like this, I go straight to Pliny the Elder, whose Naturalis Historia documented everything the Romans knew about the natural world with encyclopedic thoroughness. However, with nutmeg it's a little bit hazy. He talks about plants that may be nutmeg, but really we're not sure what he could be referring to. Here he talks about something called comacum:
In Syria, too, is produced that kind of cinnamon which is also known as comacum. This is a juice which is extracted from a nut, and very different from the extract of the real cinnamomum, though it somewhat resembles it in its agreeable smell. The price at which it sells is forty asses per pound. Source
It certainly sounds like he could be talking about nutmeg, but nutmeg is in fact native to India, not Syria, which leads some scholars to dismiss comacum as something else. It seems, then, that the Romans didn't know too much about nutmeg, if they knew it at all. It wasn't until the 6th century that nutmeg was introduced at the Byzantine court, and Ibn-Sīnā (Avicenna) wrote about nutmeg around the year 1000 in present-day Iran.
When it did arrive in Europe, most apothecaries were hesitant to recommend it as a spice for food due to its hallucinogenic properties. But it was often used as perfume or medicine. It was very expensive—a pound of nutmeg cost about half the price of a cow in England in the 14th century.