I have lived in E. TN....
Now, of course, this is not usual, but the biggest snow storm on record in E. TN with as much as three feet of snow was actually on March 13th. It is still 'winter' until April. You will not see leaves and flowers until May at any higher elevations.
Unless Dollywood and other attractions move up their opening dates as early as your scheduled 'spring break' then things could still be closed. I have been in April during good weather, and it was very nice! (I just checked their website, and they do not have next years schedule posted, but this year they first opened for the weekend of March 28th-30 I do remember hearing that they were going to cut back on days and hours because of the economy, etc...
I wouldn't be too awfully worried about ice and snow, which can be possible but not probable... But, yes, I would want to make sure that you are realistic in your expectations about what you want to do, traveling off-season, etc.