I think it is also important to keep in mind that Regina truly trusted Snow White, and was fond of her. If it is thought over carefully, Regina could not have anyone to truly confide in–her mother was(of course) never an option, and her father probably wouldn’t have been able to keep it to himself for long. Cora was incredibly powerful, and if she knew that Henry knew something, she would have gotten the information out of him. Of course she had Daniel to talk to, but she didn’t seem to be able to see him as often as she would have liked, and it didn’t look as though she had many friends.
The way she talked to Snow White about True Love was with great energy–I think it felt great for her to have someone to talk to, even if that someone was ten years younger and a child, she still was able to explain her feelings in a way that she would never have been able to explain to her mother without consequence.