Yes, there were supposedly Irish monks on Iceland and the Faeroes. St Brendan was claimed to have travelled to America. He certainly visited quite a few islands, given his story, but by the standards of the day, that might just mean he took a week's cruise round the Hebrides!
A Roman admiral took his fleet round the coast of Scotland, as part of General Agricola's campaign against the Picts (don't remember the year). However this means little, as it was coastal sailing and a voyage across the Atlantic is obviously a different prospect. Even on a coastal trip, the waters of the Pentland firth and Cape Wrath must have been pretty terrifying to Mediterranean sailors, so I can't see them having stomach for more.
As for trade with Norway, sure the Romans had trading routes with many areas outside the empire, Ireland as well (they may even have invaded Ireland at one point) but the trade would be carried out by local craft, probably not dissimilar to the Viking trading ships of a few hundred years later.