HKEY_CURRENT_USER \ Software \ Microsoft \ Windows \ CurrentVersion \ UnreadMail \ <Account> \ MessageCount and set Data value to 0x00000000 (0)
To remove all unread e-mail counter messages from Welcome logon screen, go to:
HKEY_CURRENT_USER \ Software \ Microsoft \ Windows \ CurrentVersion \ UnreadMail \ MessageExpiryDays and set Data value to 0x00000000 (0) [0 = Disabled / 1 = 1 day / ... / 3 = 3 days (default setting)]
If the key does not exist, create a new entry, i.e., MessageExpiryDays REG_DWORD 0x00000000 (0)
I don't know if there's a way to stop the message for just the Hotmail account.
If you don't have any e-mail accounts to automatically download into your client (Outlook or other), it's probably harmless.
If you experience any difficulties, you can just recreate the key and the two values shown in my screenshot. Subkeys for accounts will automatically be created when you set up your e-mail client (actually the whole UnreadMail key would probably be created).