Yes. Swiss Miss Milk Chocolate Hot Cocoa mix does in fact expire. According to EatByDate, Swiss Miss Packages lasts for 6-12 months.
The shelf life of cocoa is influenced mainly by the best before date and how it is stored. If pure cocoa is stored properly, it does not really go bad, but the flavor and quality do decrease over time. Instant hot chocolate mixes, on the other hand, usually contain powdered milk (or some type of dairy product) so they they do actually expire and go bad.
Swiss Miss Milk Chocolate Hot Cocoa mix, like a lot of other sweets, has usually a "best by date" which is simply the last day that a manufacturer will vouch for optimal quality and flavor, not safety.
If the cocoa has remained dry and looks fine, then your sense of taste is the best way to tell if it is still good. When cocoa is no longer good, the chocolate taste in the powder disappears.
Cocoa should be kept in a cool dry place like the pantry. The original container is fine, as long as it is properly re-sealed after each use. Like most other foods, it is susceptible to oxidation so the less it is exposed to air the better. Also remember to use a clean spoon or pour your powder into your cup to avoid cross contamination. In humid environments, it may form clumps within the dry powder and expire sooner.
Find interesting facts about cocoa at EatByDate.