If your mods are there, which they should be, then you will see them running in game. (program files(likely x86) / steam / steam apps / common / skyrim SE / data), you will see your mods installed there.
Just out of interest, how do you know that no mod loaded? Some mods require other programs, like mods that have scripts may require the script extender mod/tool, which will allow the mod to run without issues, such as CTDs (crashes to desktop).Ĭurrently, Special edition doesn't have the script extender tool made for it yet, so at least you can eliminate that issue, but it's good to know. You have to make sure that they are all plying nice together. It's not a simple case of plug them in and play.
If you're new to modding, a good thing to do is watch some tutorials over on youtube, to familiarise yourself with installing mods, and testing them - seeing how they load with others - in the game.