Within a view listing, how can I denote whether a node's date is upcoming, current or past?
A possible solution is to use the Views feature "rewrite result" (as explained also in Rewriting view fields), combined with the Views PHP module.

If you're not experienced in PHP, you may want to experiment with only the "rewrite result" feature, which may help to come up with an acceptable compromise for what you're looking for.;

Note: The Views PHP module only has an alfa version as of today, but it's used in about 70K sites anyway ... That many sites can't be wrong, right?