With the current version (v1.0.7) of Thunderbird, you're pretty much out of luck with Hotmail - and most other webmail providers. Thunderbird and Hotmail/webmail more or less don't natively support one another, though you should be able to use
Firefox to view your Hotmail web account to view, send, and manipulate messages. See the
Thunderbird FAQ.
A
Thunderbird Webmail Extension providing
some webmail functionality is available, though again, the v1.0.7 (and prior) version(s) of Thunderbird won't work with many webmail hosts. See MozillaZine:
Using webmail with your email client.
The upcoming (in the very near future - the almost-
final release candidate is now in the field) v1.5 Firefox/Thunderbird release is intended - among other bells, whistles, tweaks, fixes, and updates, to handle webmail quite a bit better than v1.0.7 and prior releases. So far, it kinda sorta pretty much almost does - still needs work, though.
I don't recommend trying most Betas - even near-final or final release candidates - for most folks in most circumstances. There are exceptions,
Microsoft Antispyware Beta particularly notable among them, but other than the very few exceptions, Beta software generally is not a good idea for casual users to tackle; the whole idea behind Betas is to find, expose, and correct bugs, glitches, and vulnerabilities before turning the product loose on the public. The current-as-of-this-writing Firefox/Thunderbird v1.5 Beta, though reportedly very nearly ready for general public release, is still buggier, trickier, less stable, and more unpredictable than most normal folks want to deal with. I know its still full of eyebrow-lifting surprises for me ... not many hair-tearers anymore, but lotsa eyebrow-lifters.