Thoughts: Ok, Dollywood, as with most all themepark/amusement parks will not allow firearms.
Remember: In Tennessee, the sign must be a "gun buster" sign. You will also have the rights a Tennessee HCP has. Please go to the State's HCP website for clarification.
Also, go to TNGunowners.com and look in their section on who is posted, and see if any of the restaurants or tourist traps, erm, tourist spots you want to visit are listed.
Always have a place to secure and hide the firearm in your car. Worst case, go spend around $25 on a portable gun safe with tether at Academy Sporting Goods, or other place.
Herschend Family Entertainment Corporation doesn't post their property, but they do ban firearms in their rules (which you only see if you ask, or go looking for them).
The Herschend brothers (Jack and Pete) are big "family values" socially conservative Republicans, but Pete fought against concealed carry in Missouri, and made sure amusement parks were included as places off limits.