Why weren't you on top of her electronic/social media/phone use in the first place? Young children and young teens should have NO expectation of privacy on their electronics. Parents should be monitoring, and kids should know and expect that this will be occurring.
While liking a boy and wanting to be in social settings with her friends and this boy are all normal and developmentally appropriate, it seems you need to start talking to your daughter more about the things to come. It's all innocent now, just a hug. But does she know what to do when a boy tries to touch her in other places? Will she know how to stop when a boy she really likes wants to kiss her and then wants to take it further? Can she say the words and not just freeze? You have to prepare her because without knowledge, kids, even really great kids, find themselves in situations where they're just in over their heads. And they don't know what to do or how to get themselves out of it.
Again, this hug was very innocent, but do you want your daughter texting photos of herself hugging boys at this age? Even though this was an innocent photo, does she realize that once she texts something, it's out of her hands and can be sent anywhere to anyone? That one of her friends could put it on their social media? If this happens, the message is now out of your daughter's hands, and pictures on social media can take on a life of their own and turn into something that was not originally intended. I'm not saying hugging a friend is wrong, but it seems like she (and many other teens and tweens who do the same thing) put photos like this out there because they want validation from others. With your daughter, maybe this "message," is, perhaps, that she is popular, that she's with a certain group, or just to let others to know that this is "her" guy.
You're not her friend. You're her parent, and you have to make that distinction and do the parenting you need to do. Yes, she will cry. Get ready for it. Tween and teen girls cry. They cry when they're hurt, when they're angry, and sometimes just because. She will get mad at you at times. You cannot let her anger or tears prevent you from doing what you need to do as a parent.
Talk to her. Make sure she has the facts and understands how her body works. Make sure she knows what your expectations are as far as real dating for when that time comes (what they're doing now isn't really dating; it's a completely normal part of tween development when they meet in groups in social settings like skating rinks). Make sure she understands what your expectations are as far as physical contact with boys. Teach her boundaries regarding her body. These talks need to be open and ongoing dialogues. It's not a one-time thing, but rather, a continuing part of the growth of your mother-daughter relationship. As she grows and matures, make sure she knows what your expectations are regarding sexual activity. Empower her to protect herself and her body.
Wanting to meet up with her friends (including this boy), at the skating rink, is a normal part of her development Tell her you realize that, but at the same time talk about your expectations for her behavior in those settings. Acknowledge her feelings, even if you don't understand or agree with them, and let her know there is nothing that she can't tell or ask you.
As for this boy, you can't really "break them up" because they're not truly a couple. They are young, preteens who like each other. In a few months, this could all change, and he may like another girl, or she may like a different boy. Just make sure that you are there for her as the strong support she needs as she goes through these new and often challenging experiences of the tween/teen years.