The dates and times used by Email are UTC. This means that for Thunderbird to set up the correct date and time on emails your operating system must be set to the correct timezone and daylight saving settings.
Simply because the little clock on the bottom right of your screen shows the correct time does not mean your time zone is correctly set.
Instructions for changing the timezone are;
XP Vista Windows 7 and Windows 8 OSX
Thunderbird has only ever displayed the time on messages for today. The logic involved is fairly simple. It makes todays messages easier to identify in the list, and you don't need to be shown todays date as you already know it.
If for some reason your feel you must have a date MozillaZine have detailed instructions on overriding date and time formats in Thunderbird.