New York City's latitude is 40.7128° N, while Rome's latitude is 41.8919° N.
Despite the common belief that warm water transported north via the Gulf Stream is responsible for Western Europeās milder winters (to the tune of 15°C ish), a concept first popularised in 1855:
One of the benign offices of the Gulf Stream is to convey heat from the Gulf of Mexico, where otherwise it would become excessive, and to disperse it in regions beyond the Atlantic for the amelioration of the climates of the British Isles and of all Western Europe.
Itās influence is apparently minor below latitudes of 60° N. Northwards of 60° N it contributes roughly a quarter of the difference between temperatures by preventing the formation of ice. However, the largest contributing factor to the difference in temperatures across the Atlantic Ocean both north and south of 60° N is atmospheric advection around the Icelandic Low.
[...] transport of heat by the ocean has little influence on the contrast between the mild winters of western Europe south of 60°N and the harsh ones of eastern North America. North of 60°N the OHT (ocean heat transfer) accounts for about a quarter of the contrast by restricting winter sea-ice cover. The dominant cause of the contrast, at both latitudes, is atmospheric advection around the Icelandic Low and the simple maritimeācontinental climate distinction. The exact positioning and strength of the Icelandic Low is important to the climate contrast and is shown to be greatly influenced by the orographic forcing of the Rocky Mountains. Therefore, the difference in the winter climates arises fundamentally through atmospheric processes and the seasonal storage and release of heat by the ocean mixed layer. This is also all that is required to establish the difference in winter climates between the west coast of Europe and the west coast of North America at the same latitudes.