HeavyWeaponsGuy
Banned
I doubt that they would freeze to death as Roman troops fought in Britain and Germany . By building a fortified camp they would have protection against the elements and would be able to stockpile wood to burn. For the sake of argument they would at least need a base in which they could carry out repairs to their ships and it would have to be strong enough to hold against any threat.
I would suppose that perhaps a small expedition might be sent southward down the coast to Maryland or Virgina region to see if conditions might be better to eventually relocate the Roman settlement to there.
It is possible that some of the ships might have had grain seed aboard.
Staten Island would be the place that I see them picking not Manhattan.
Okay cool they have a fort, that will help them not get killed in the short term by natives with whom they cannot communicate and have never gone to war with before, this means no espionage (if you intercept any sort of signal or message you don't understand it, back to square one) and you can't make peace and you can't call their tactics.
Their supplies better last too, unless they can learn to get food in alien territory and grow crops that they've never eaten (actually forget eating, they never even cultivated these) before.
What is the sentiment back in Rome that allows for this colonial venture to proceed? It's expensive and as far as they know they aren't getting any readily available returns on their investments, they aren't going to get South American gold in modern day New York. Things like tobacco and cotton will probably only be a strange curiosity unless some kind person sits down a Roman (senator or emperor, whatever time this happens) and explains that this weird leafy stuff you put in a pipe tastes nice and feels good if you smoke it and that cotton makes for good clothing. Rome isn't going to be immediately convinced of the need to send more and more of its citizens abroad to godforsaken lands abroad, especially once it becomes clear that the land is hostile and alien. Rome is an advanced civilization but its rulers may well lose heart when they hear of horrible new diseases and plagues killing their citizens that they have no recourse against unlike more domestic stuff.