Your email accounts can be added in Apple Mail and in System Preferences > Internet Accounts.
Deleting an account in either Mail or System Preferences does not actually delete the data.
1) check in Mail > Preferences > Accounts - do you see the account listed but inactive?
2) check in System Preferences > Internet Accounts - do you see the account listed? Is Mail checked?
Go to User's Library (see below)
Scroll down to Mail folder.
In V3 folder you will see several folders. For some users you will see actual names to know what account and others see a number/lettering name.
Check in each folder to find your Hotmail messages. If you have specific folders in Hotmail this might make it easier to determine.
If the accounts are not listed in either Mail or System Preferences > Internet Accounts and there is no data folder in V3 for hotmail, then try resetting Mail back to defaults.
(note before renaming Mail folder, check to see if you have messages stored under the local "On My Mac" folders. If yes, you need to export these first. You can import later but it's easier to export plus you have better results. Also do you have Time Machine backups?
1) In System Preferences > Internet Accounts uncheck Mail option for your me.com account plus any other email accounts you might have listed.
2) Rename the Mail folder in the User's Library to MailXXX
3) Move to the trash the following files in your User's Library:
Scroll to Containers, delete com.apple.mail (folder)
Scroll to Preferences folder: delete the following
com.apple.accounts.plist (file)
com.apple.accountsd.plist (file)
com.apple.mail-shared.plist (file)
com.apple.mail.plist (file)
MobileMeAccounts.plist
Log out under the Apple in the Menu bar.
Log in
Empty the Trash
Go to System Preferences > Internet Accounts
Check Mail for your me.com account.
Open Mail
Mail should open with the all new files in the User's Library > Mail folder.
Now try adding your Hotmail account in either Mail > Preferences or System Preferences > Internet Accounts
Note: To add Hotmail select Add other Account. If it does not default to IMAP, I suggest you switch to IMAP!
Incoming Server: imap-mail.outlook.com (Use SSL)
Outgoing Server: smtp-mail.outlook.com (Use SSL, Port: 587, use authentication > password.)
Show User's Library
The User's Library folder is hidden by default. To unhide: Select the Finder in the Dock. Under Go in the Menu bar > hold down the Option key and you’ll see the Library.
Finding the User Library Folder
http://www.takecontrolbooks.com/resources/0167/site/chap11.html#FindingtheUserLi braryFolder