It looks like you'll be able to keep using a lot of your favourite mods on the Skyrim Special Edition.
Skyrim Special Edition will support existing mods
Bethesda announced Skyrim Special Edition during their E3 showcase. Soon after the show, Skyrim fan Kyle Rebel asked Bethesda's Pete Hines, via Twitter, whether the PC version would support existing mods or not. Hines responded "Basically, yes".
— Kyle Rebel (@Rebelzize) June 13, 2016
— Pete Hines (@DCDeacon) June 13, 2016
The 'basically' qualifier here seems to indicate that some additional work will need to be done by modders to get their mods working on the new engine...although that's largely speculative at the moment.