However, it's impossible to recover your previous set up manually, which is why I highly recommend that you download NMM from the front page of the Nexus site and use it for any mods you download and install. Nearly all modders have installation instructions on how to install their mods manually, which is a fairly simple process once you've learned where your Skyrim folder is located.
Not all mods by Nexus will appears in your Data Files or Load Order section, as they have no. Nexus mods are installed manually into Skyrim by you or installed comprehensibly by the Nexus Mod Manager. Steam uses a subscription system to install those mods to your game through a cloud.