Without specifics of when and exactly where in the Arctic your character plans to visit, this is a difficult question to answer.
I see no risks (beyond the usual storms etc.) of sailing a boat of pretty much any description in the tropics and higher latitude ice-free waters.
The Arctic covers a lot of territory on water and on land, some of which is ice free for much of the year and other places are completely ice-bound all year around (the geographic pole generally is, no matter the time of year). There are also historical and present-day fluctuations in ice cover area and accessibility for much of the Arctic, which have allowed navigation of things like the North-West Passage in recent times, which were historically difficult, if not impossible. Significant cities of Northern Europe are within the Arctic circle and certainly have shipping year-round.
However, ships of all sizes and shapes have been sailed in the Arctic before, ranging from seal-skin covered kayaks by the Inuit and related peoples, to large modern metal container and tanker ships in recent years. The Vikings in their colonization and settlement of places like Iceland and Greenland certainly navigated Arctic territory in open wooden monohulls. There are many well known exploration expeditions that took place in the late 1800's and early 1900's that used wooden sailing ships (monohulls as far as I know), some of which were iron-reinforced to allow greater strength against the ice. Modern ice-breaker ships, which are also monohulls are capable of handling ice that is several meters in thickness.
As to whether a catamaran or trimaran would be better for these regions, that is a question which a more knowledgeable sailor might be able to answer. However, I would guess that these are more at risk of structural failure or being caught in the ice - navigating open passages with ice in them is hard, even with a monohull, where you don't have to worry about hitting ice with more than one hull.
Catamarans are used in the Arctic for some purposes according to this article, but these seem to be largely lightweight ones used for exploration rather than transport.