In Thunderbird, there's a way to customize the display of the date header in your inbox.

Short answer: Go http://kb.mozillazine.org/Date_display_format and follow instructions

Long answer:

1. Edit > Preferences > Advanced > Config Editor
2. Type 'dateformat' in the search box and hit enter.
3. If the following 3 entries do not appear, you'll have to create them.

mail.ui.display.dateformat.today
mail.ui.display.dateformat.thisweek
mail.ui.display.dateformat.default

4. Right click in the empty space of the results pane. A menu will appear.
New > Integer
Preference name: mail.ui.display.dateformat.today
Preference value: 0
New > Integer
Preference name: mail.ui.display.dateformat.thisweek
Preference value: 4
New > Integer
Preference name: mail.ui.display.dateformat.default
Preference value: 2

5. If you already have these config entries, just change the values to match what I have above.

What this does is:

1. For messages received today, displays only the time (e.g. 10:15am):.
2. For messages received this week, displays day and time (e.g. Friday 10:15am)
3. For all other messages, use the long form (mm/dd/yyyy)