Yeah, it's probably java, but hotmail's MS's animal, so for all we know, it could be that they're blocking anything but IE! (Just joking, MS isn't that good.
This is the "mozilla" way, because that's what I use. When you use the automatic install thing that pops up for mozilla, it sends you to a page, you download for a while, then possibly close and reopen mozilla. Nothing, right?
The problem is, if you're using a fairly new version of Linux, the browser is compiled against a different set of libraries. What you need to do is set your /whatever/mozilla/plugins link 'libjavaplugin_oji.so' to point to a different java directory than the one it "naturally" points to.
The one it defaults to is(with a lot of potential variation):
Your distro is a new one, so what it should point to is:
delete the java link in your mozilla/plugins directory, then 'man ln' should help you with your details, but the general form is:
ln -s TARGET LINK_NAME
Hope this helps. I know it frustrated me for a long time.