As hildajenniJ says, it really is confusing. Have you tried to access your Hotmail account by logging on to it over the internet rather than using the email app on your computer? Don't click any links from your email but use your browser to look up Hotmail login. Can you read your emails there? From some of the information I've read looking this up, accessing your mails directly using the web every couple of months is the way to ensure your Hotmail account is kept 'live'.
Have you been sent a link in the email to click so you can 'login' to your mails? If you have, it is likely to be a scam. If it is giving you information without any links, it may be genuine.
If you are stuck, I think it might be worth contacting Microsoft support too.