Yes, hot chocolate does expire.
But that also depends on what kind of hot chocolate we’re talking about.
Hot chocolate made from scratch i.e. from cacao powder then most likely it won’t technically expire. It’ll just taste funny and won’t be as fresh.
Instant hot chocolates, typically contain milk-derived products, you need to know that it will eventually expire.
Check the expiration date on the package
Hot cocoa mix, whether it comes in a packet, canister, or other container-type, will typically expire within a year or two. Check the printed date on the label to know for sure.