I had the same problem to when I migrated to OSX. If you have a new computer or have newly placed a new OS on your mac, then you will need to log onto your hotmail off Safari or whatever internet browser you use from your new computer or newly updated OS computer and "re-logon" to hotmail. They will ask you to enter your security question since you are logging in using a "different" computer or location and voila hotmail will not block your smtp anymore.
So now, just go back into mail and see if you can send mail through your smtp outgoing hotmail server. This should work.
The other thing is, try again tomorrow or later to resend because the stmp server for hotmail is finicky and goes down from time to time. It's nothing to do with your OS Mail or your settings so you won't need to go changing all that around. Try this easy fix before you try the complicated fixes.
iOS: Unable to send or receive email
Can’t Send Emails on iPad – Troubleshooting Steps
Setting up and troubleshooting Mail
Try this first - Reset the iPad by holding down on the Sleep and Home buttons at the same time for about 10-15 seconds until the Apple Logo appears - ignore the red slider - let go of the buttons. (This is equivalent to rebooting your computer.)
Or this - Delete the account in Mail and then set it up again. Settings->Mail, Contacts, Calendars -> Accounts Tap on the Account, then on the red button that says Remove Account.