From MozillaZine Knowledge Base
You no longer need to use an add-on to use Hotmail with Thunderbird. Create a new account by pressing the Add Mail Account button in Tools -> Account Settings -> Account Actions.
If you want a POP account use:
It currently defaults to creating a POP account. If you want a IMAP account you need to press the Manual button in the second screen of the account wizard and edit the settings until the remote database is updated to support IMAP. 
You can still use the webmail extension and its Hotmail add-on. However, the webmail extension is slower, harder to configure and may break (requiring you to get an updated add-on) whenever the web page changes. Normally you'd only use it if you're behind a firewall that prevents you from accessing the POP server or you need to download the contents of the Spam folder.
You need to login periodically to keep Microsoft from disabling the account. You don't need to do this using a browser, Thunderbird will login to Hotmail/Outlook whenever it checks for new mail. If an account suddenly stops working take a look at Outlook down detector
Switching to Outlook.com
Microsoft is slowly replacing Hotmail webmail with Outlook.com webmail. If you already have a Hotmail account that works with Thunderbird you can switch between the Hotmail and Outlook webmail using the gear icon in the upper right corner (of their web page). You don't need to make any changes in Thunderbird since Outlook.com uses the same POP and SMTP servers as Hotmail.
If you want to switch to a Outlook.com email address first switch to Outlook.com webmail. If you haven't already specified an alternate email address that can be used to get a new password if you forgot yours, do so. That email address may be needed for you to confirm your changes (prove its you who is doing that) . You can add this email address by clicking the gear icon in the upper right corner, click More mail settings, Account details, and then select security info.
Then click the gear icon in the upper right corner, click More mail settings and Rename your email address. You will be prompted to login again. Use the old username when creating the new outlook.com account. It will ask you what to do with Hotmail mail (either put it into the inbox or in a separate folder).
In Thunderbird delete the saved Hotmail passwords using Tools -> Options -> Security -> Passwords -> Saved Passwords. Change the Hotmail email address to the Outlook.com email address in Tools -> Account Settings -> Hotmail -> email address, Tools -> Account Settings -> Hotmail -> Server Settings -> Username, and Tools -> Account Settings -> Outgoing Server (SMTP) -> Hotmail -> Edit -> Username
Exit Thunderbird and restart. It will prompt you for the new password. Enter it and check the box to save it in the password wizard. You're done.
The Outlook SMTP server may replace the display name in your From: address with the name you registered with your Microsoft account. This post claims this only occurs if the recipient uses the Outlook email client but the problem has been reproduced using Thunderbird to send and receive the message.
Hotmail and Outlook used to work the same. Recently however Hotmail accounts started losing connections. If this happens to you the workaround is to add an alias for outlook.com. "An alias is an additional email address that uses the same inbox, contact list, and account settings as the primary alias. You can sign in to your account with any alias—they all use the same password." 
Hotmail had a design flaw where if you created a password longer than 16 characters it would work with webmail, but would fail when you used a email client. The problem effected other email clients such as Windows Live Mail, it was not Thunderbird specific. The problem was due to the Hotmail web page for setting the password only saving 16 characters, regardless of how many you entered. If you logged into webmail it automatically truncated what you entered to 16 characters, so that worked. When you tried to login using Thunderbird it passed the full password, which does not match what Hotmail expects, because Hotmail only stored up to 16 characters.
The workaround was to login to Hotmail using a browser and change the password to one that isn't longer than 16 characters, delete the saved password using Tools -> Options -> Security -> Passwords -> Saved Passwords and then restart Thunderbird. When you are prompted for the password enter it and check the checkbox to save it. 
The problem has been fixed by Hotmail (and also Outlook.com) now limiting the maximum password length to 16 characters.
SSL Security Errors
Some people are reporting occasional SSL security errors with Hotmail. When that happens you want to verify that you're actually connecting to who you think you are, and if so let Thunderbird create a security exception so that it doesn't warn you every time.
Some other companies (mainly ISPs) run a customized version of Hotmail using their domain on mail servers provided by Microsoft. Its been suggested that Microsoft is using a round robin DNS server that causes it to occasionally connect a email client to a third party Hotmail server instead of one from Microsoft. If that happened you would get a SSL security error due to the domain in the SSL certificate not being live.com. However, plenty of people using Hotmail never run into this problem.
Exceeded the login limit for a 15 minute period errors
If you login too often (due to checking for new mail) you may get a The STAT command did not succeed. Error getting message number and sizes. Mail server pop3.live.com responded: Exceeded the login limit for a 15 minute period. Reduce the frequency of requests to the POP3 server error message.
The login limit is enforced by the server, and doesn't appear to be documented. This problem occurs with other email clients too, but doesn't occur with any Microsoft email clients. There isn't any known workaround. Reducing how often Thunderbird checks for new mail in Tools -> Account Settings -> Server Settings -> Check for new mail every X minutes" helps. 
Hotmail is starting to roll out support for sending and receiving email from other email addresses, including Gmail and Yahoo. This is similar to what you can already do with Gmail and Gmx.com You need to register and validate the email address with a Windows Live ID. See this article for more information.
If Hotmail detects that Thunderbird is configured not to "leave messages on server" after checking for new mail it will not delete the message on the mail server. Instead it will move it to a temporary webmail folder. You can disable this feature by logging into Hotmail webmail using a browser, selecting options, "POP and deleting downloaded messages", "Do what my other program says-if it says to delete messages, then delete them." and then press the Save button.