Is it fine to exclude an email salutation for short messages?
An important thing to note here is that often these dropped headers don't happen because the email is merely short, but usually because the email chain starts to approximate a conversation, i.e. a quick succession of short replies. So the formalities shift from those of writing letters to those of talking in person. So maybe take some cues from there.
In particular, even if it is short, not starting the first message with some greeting would be a bit impolite. The same is true if some time has passed between messages. (You'd greet somebody if you meet them again, even if you just met them yesterday and didn't talk to anyone in between) But a quick ABAB-exchange within a few minutes doesn't really warrant repeated greetings.
And of course, as mentioned in the other answer, when in doubt, just err on the formal side.