Your ex-gf/bf messages "Happy Valentines Day"

Mhm. That kinda depends, anyway. Especially who broke up with whom, and how. The issue about whether you're supposed to stay friends with exes or not is kinda up in the air, anyway; some research suggests mostly psychopaths stay friends because they can turn emotions on and off on demand and they may still be able to get something out of it. In any case practically everybody agrees you need to stay off-contact for undefined time after breakup. So if it's that kind of situation, that would affect the response.
For women, it's obviously somewhat easier and more expected to keep guys as "let's just be friends" to go for emotional support when things go wrong elsewhere, without expectation of things going sexual; whether this is right or not. Again, it depends how you feel about this sort of thing, how your potential new partner feels about an ex hanging along, if the context, their current dating status or their personality suggests it's just a courtesy, if they want a shoulder to lean on, or are possibly looking for more.
Soo... yeah, like, too little information to give any sort of answer. Proper response in any case is probably just "Thanks, happy Valentine's day to you as well."