I'm late to the game, but I totally agree with this. I also think that Snow (at least past Snow, I can't really say much for Season 3 Snow) is so caring and compassionate and is not only concerned for Emma at this point, but is also being compassionate toward Belle because Emma and David were able to find Rumple in the woods but were not able to bring him back to her. He is still under Zelena's control and Snow knows this is hard for Belle. I've never really thought of Snow and Belle as being particularly close, but Snow's nature (and Mary Margaret's, for that matter) is to be compassionate.