There are plenty of downsides for doing it this way and I dont suggest doing it and just waiting for the mod authors to port the mods normally but it IS possible to use certain older mods with the Special Edition. New quests, environments, characters, dialogue, armor. Skyrim Special Edition also brings the full power of mods to the PC and consoles.
Any mod that uses scripts will require a script extender to work and currently a script extender for SE is not out so they will not work at all, but any mod that does not use scripts and is only an esp file will work just fine as long as you place it in the skyrim data folder and enable it in the mod menu or mod manager of your choice, also a mod that uses no scripts but has a bsa archive will not work out of the box because the SE uses a different archiving system more similar to Fallout 4's, BUT if you extract the archive using a mod manager and then install the extracted files directly into the data folder for SkyrimSE it will work for most mods. The Special Edition includes the critically acclaimed game and add-ons with all-new features like remastered art and effects, volumetric god rays, dynamic depth of field, screen-space reflections, and more. The short answer is no most will not, however certain mods will work, let me go into a little bit of detail. The 'Best Answer' is actually kind of misleading and not entirely true.
