If you are auto sending all emails in both HTML and Plain Text then the recipient could be Viewing in Plain Text and has not selected the option to display emotions as graphics.

In Thunderbird this would be located here: 'Tools' > 'Options' > 'Display' > 'Formatting' tab or 'Menu icon' > 'Options' > 'Options' > 'Display' > 'Formatting' tab

Plain Text messages:

• select: 'display emotions as graphics'
• click on OK

It still does not work - the emoticon does not even show up in my sent mail.

Traditionally, what we have come to call "emoticons" are indeed just "little signs". They were designed to be composed from the keyboard and used in text-only environments.

•  :-D is a laugh out loud
•  :-) is a smile
•  ;-) is a wink
•  :-( is unhappy

etc.

Any software can choose, if it wishes, to portray any of these as a graphical symbol, but what is sent is the sequence of characters. Your correspondents' software may choose to convert them to images, or it may show them as characters. You have no influence over that.

I am puzzled by you not seeing them in your own messages. If you have a toolbar showing the yellow faces then you are already composing using HTML and we'd expect to see the graphics in your outgoing message. Perhaps there is nothing else in the message that requires fancy formatting and so Thunderbird is downscaling it to plain text. But even so, that occurs, I think, at the point of sending and I'd expect still to see the graphics whilst composing.

re :the emoticon does not even show up in my sent mail. click on 'Sent' folder select the email.

Check setting: 'View' > 'Message body as' > 'Original HTML'