When it comes to what is socially accepted in the US, ice is mostly reserved for the harsher stuff like bourbon and scotch. The ice serves a purpose of diluting the liquor, thus making it smoother on the way down. It serves a purpose for different whiskies that have harsher spice notes.
Tequila, vodka, brandy, cognac, and rum should be put in the freezer rather than mixed with ice (unless in a mixed drink). This isn't to say ice will ruin any of these drinks, but more so that they are generally considered to be smoother and thus do not need ice. While spiced rum might be harsher than the rest, it is still kept in the freezer with the other rums.
That being said, it's all personal preference. Drink it the way you like it!