mutt aliases can be converted to ldif format to allow them to be imported to address books that support ldif such as the address book that ships with thunderbird.
Install abook. abook ships with gutsy.

# apt-get install abook

Convert your mutt aliases file with abook to ldif

# abook --convert --infile ~/.mutt/aliases \
    --informat mutt \
    --outfile ~/aliases.ldif \
    --outformat ldif

My mutt aliases file is located in ~/.mutt/aliases. Ive chosen ~/aliases.ldif to store my aliases file. Your address book of choice should be able to import ~/aliases.ldif.