Here is how a tech support guy from Microsoft told me how I could close my email account [hotmail], and still be able to use MSN Messenger.
Since you have the privilege of accessing your Hotmail account through mobile, hence please close this mobile access before you close your Hotmail account.
1) After you start your Internet explorer, visit the link:
2) Sign-in with your username and password
3) Click "Delete my account" under "My account"
4) Click "Delete" button on the new page to confirm
Now you can close your Hotmail account by following the steps given below:
1. In the upper right corner of your Hotmail account page, click "Help"
2. In the MSN Hotmail help window, click "Find" and type, "Close account", and then click "Go"
3. In the search results, click the "Close your Hotmail account" link
4. Follow the instructions to close your Hotmail account
Please note that you can also close your free Hotmail account by not signing in to the account for 30 days or within the first 10 days after you set up the account. Hotmail then marks your account as "Inactive", your stored messages are permanently deleted, and inbound messages are returned to the sender. You can activate your account by going to the sign-in page and typing your sign-in name and password.