HI.
We recently faced a similar question - not about a complex survey just about smilies like you see them on airport toilets or in hotels... For this I wrote a simple php / MySQL survey running on a public facing server. After this I added a line with smilies (good, neutral, bad) into the ticket closure eMail we send using the auto-close feature.
Another option is to call a link to a survey system like lime-survey.
Thanks.
Oliver