My thoughts about this are that Jen wanted to show that Emma trusted Snow and felt at ease with her; felt she could be herself. Since she was only this way with Snow in S1 (actually only with Snow through the whole series now that I think about it), I thought Emma subconsciously picked up on that mother/daughter connection between them. I also noticed that Snow was drawn to Emma right off. I mean, Snow barely knew Emma and invited her to live with her. I love the way they played it in S1. They knew they were connected in some way and just immediately felt comfortable with each other.