/etc/aliases is nothing more than just a file (database) with e-mail aliases. In order for these mail aliases
to be actually used, you of course need a mail server program.
Check if "sendmail", "postfix" or anything alike is installed and running on your system.
Typically, you can do this by running:
and checking for the programs above (they should have got an "on" for levels 3-4-5 at least.
"/sbin/service <service_name> status" may also work (for valid service names, do "ls /etc/init.d"
To try your Linux to hotmail alias, you could also just set it up in /etc/aliases and try it out.
/var/log/maillog or something like that may give you a clue on what's going on/what's going wrong.