It should be 100% work, most of the companies I've worked for policies against using it for personal reasons or at least thrown against the idea.
Where I'm currently working at the moment, the time and effort we (IT) have to spend because people have used their work e-mails for personal reasons is unbelievable. from spam, viruses to re-opening mail boxes etc.
Don't forget that companies have the right to monitor your emails, so why would you want to use it for personal reasons when hotmail/gmail is free and can be accessible from any device.