You sign up for the newsletters on
Dollywood and/or
Dollywood's Splash Country's website. Should sign up for both because they are separate email lists I think. As far as getting the surveys I'm not sure how that is picked. From the ones that Screamscape has reported as being out and compared to what I have known of people getting them not everyone will get the survey. It is either random or some type of demographic thing I guess, really not sure how they pick who gets them and who doesn't.
I remember one year (2001) my family actually participated in a survey at the park. We were in Dreamland Forest the year it opened and a host asked us questions about three concepts for the country Fair area remodeling. And beleive it or not from what I remember what is now the Country Fair was not a concept itself. What we see now as the Country Fair is a mixture and at least one idea ride that was presented as an idea for the Country Fair ended up somewhere else on park.