I have only installed one Mod in Skyrim (The retexture mod in Steam) and it worked.
I have not tested ENB or anything else.
I've read that a lot of mods work really well, but the more mods the more bugs.
To install Mods, I think you just have to download the esp file and put it in the correct directory. If the mod has an installer, just use PlayOnLinux Configure and go to Miscellaneous Tab and click "Run a .exe file in this virtual drive"