When thinking of this, I like to rephrase it as "do you tell your employer every minute detail of your life"?
My guessing, is no you don't! And that is perfectly fine, we, as nannies are entitled to a private life outside of work hours, as parents are too.
So, if you don't share every detail of time off work, why would you show them your whereabouts on Facebook, your thoughts, and photos?
I tend to be a nanny, that tells most things (to anyone actually) of what is going on, but there are those occasions where, my employers don't need to know what I am thinking on my status, they don't need to see photos of me at social events at weekends, they don't need to know if I have had a bad day!
We may become part of a family, but at the end of the day we will always be their employee, so for this reason alone, I chose not to befriend my employer until after I left their employment.
It is a personal choice for everyone, but my advice if you are friends with your employer, is just be careful about what you post, that they may see, and if you feel uncomfortable maybe re think about what you are posting, or maybe they are not, after all, your friend.