I have e-mail with both services:
HOTMAIL.COM
LIVE.COM
Both of the above behave as standard POP3 services. So I use Thunderbird as my local e-mail client on my Windows systems.I use the portable version, which lets me use it on different versions of Windows.
Here are some settings.
pop3.live.com port 995 using SSL/TLS standard password.
For sending mail I use the settings for my local ISP. They require that i not use any other. However, the user sees my Microsoft address and my e-mail.
Most e-mail servers will let you use a local e-mail client for pop3 stuff.
Consult the Thunderbird documentation for more information.