Rome enjoys the Mediterranean climate, meaning winters are mild, so the city sees a fairly large flow of tourists all year round, including winter. Frost and snow are quite rare during this season.
Mediterranean winter can be barely called "winter". Even in the coldest month of January, the average temperature is above 10 °C. Snow may sprinkle the city a bit, but it also melts at once. As to the rainfall, there are approximately seven to nine rainy days per month. Generally, the weather is quite favourable and pleasant to plan a vacation in Rome.