The idea is that, although emails sent to you are initially stored on your email provider's servers, some "email client" programs (eg Mail) will download copies (so they can eg let you read old emails while you're not connected to the internet) - and just because you've delete emails from Hotmail's servers, doesn't mean they've been deleted from the stores of any email clients you might've used!
If you've never used Mail with your Hotmail account, then we can eliminate that as an option - if it's never had a chance to download these emails, then we can be sure it doesn't hold copies now. But have you ever looked at the emails outside of a web browser? For example, have you ever had a phone set up to view emails?
If you've never used a non-web-based email client, then I'm afraid you're likely out of luck. Contacting Hotmail's support staff may yield results but I wouldn't bet on it.