I went online and everything I could find said that when you started the launcher you would see it telling you in the bottom right corner that it was installing and that you would get a message saying when it was done.
I had subscribed to a good 40+ mods in the workshop but whenever I would start the game the mods would never install.
Just thought I would share some advice for an annoying bug with Skyrim and the Steam Workshop not working as intended, as I think it's a common problem but I can not for the life of me find people talking about it.