Bethesda never introduced a multiplayer mode for TES V: Skyrim but the modders never gave up and now we can play the game in couch co-op, without even needing an internet connection.
The Elder Scrolls V: Skyrim has undergone enough releases to warrant memes about being played on a fridge but throughout all those incarnations, Bethesda never made it a multiplayer title. Modders on the other hand never stopped building in the efforts of giving us a multiplayer experience in Tamriel, without having to go through Elder Scrolls Online.
First, it was the Skyrim Together crew that had their share of controversies but made it possible for fans to play together online. Now, we are able to play the game together without even requiring an internet connection since Nucleus is now supporting Skyrim and therefore allows couch co-op via split-screen.
In order to get Skyrim to work in split-screen, you will need the Special Edition version of the game, which shouldn't be an issue by now since the original owners were granted SE at no extra cost.
On top of that, you will need Skyrim Together which has to be installed through Harbor launcher . Thankfully, the folks who came up with Harbor also provided a detailed guide to instal the game in the necessary fashion.
While the game will be run locally and doesn't require a connection once it's launched, you will need a way to grab all these files. If you don't have an available connection, you can also try using USB to transfer the files from a rig that previously downloaded them.