Ok - you can fire someone for something like this, but usually not fairly unless a) there is a specific facebook/internet policy that specifically states in personal time mentioning something that kind of alludes to being about work is gross misconduct - typically tribunals will find personal use of the internet at work as misconduct, and stuff outside work as irrelevant unless, say it is directly defamatory and deliberately so.
If you have complained about having a hard day I think they would lose at tribunal - might not stop them trying, but they would look like absolute idiots. Case law is pretty clear on this!
From a 'best practice' point of view they are being ridiculous.
What you MUST do now is find as many examples as you can of people at the same school, other schools in the same authority etc blogging or FBing about how they feel, including in newspaper reports, school bulletins and newsletters (eg Miss xxx was tired but happy after taking the kids to alton towers).
Especially senior people, school governers etc. NOT for blackmail but because there is awealth of case law that suggests that if misconduct is generally allowed you can't suddely say 'but not in this case'...
If you can present Governer Y said 'Phew I'm knackered after today', Teacher Z said 'looking forward to this weekend.. really looking forward', teacher D said 'good god some people are petty' etc. and that obviuoulsy this type of 'misconduct' is generally acceptable, you will be on to a win at tribunal.