Edit: I don't just say "Smile", usually there is more context to the conversation and usually ends with me trying to see if I can help fix the problem(if it's work related).
Where I'm from it's commonly meant as shorthand for "cheer up, it's not that bad" or "try to keep your chin up". Both of which actually indicate that the speaker cares about their colleague.
Said the guy who further up the thread said he "can't fathom how that could possibly be construed as sexist."
What I meant to say was that in this context I can't see how it would be construed as sexist. Or put another way... I can't see how this statement automatically defaults to being sexist absent any other indicators.
At any rate, this kind of proves my point that it's very easy for communication to come across in a manner other than the speaker intended. So serious charges like "sexist" or "racist" should not be levelled lightly.
If there is no bad intent, why should you? The answer is that a snowflake could get you fired but the rhetorical question stands.