We had this problem too. As we only allow staff to use hotmail, we've let them use Chrome instead of IE. I know that's not a solution, but you can lock Chrome down these days with Group Policy, so it's not as bad as it could have been!
SOLUTION: Make sure that in the address bar you have 'https' at the start of the URL. For some reason if you don't- you can't do anything. If it just says 'http' then stick an 's' at the end of it and you will be taken to a screen asking if you want to always use https with hotmail.
Click on ALWAYS USE HTTPS.
Select the 'Use HTTPS automatically' button and click SAVE
That should do it!!