You must be using Windows if you are getting as far as not seeing the dropdown. Adobe Reader (both 9 and 10) respects the Windows system settings for default clients.
When you go to Edit / Preferences / Internet / Internet Settings it is just opening the Windows internet settings dialog. Reader does not have one of its own.
The linked article is referring to Windows XP, where the Programs tab shows the dropdowns for each application type. Under Windows 7 this moved to the Set Programs button at the bottom of the tab in the Internet Programs section.
This will take you to the Default Programs settings page. Click Set Your Default Programs. In the list, choose Thunderbird, then click Set this program as default. This will make sure Thunderbird is selected for email in all cases where an email client can be invoked, not just when a mailto: link is clicked.