Well would you look at that? A video of someone playing Skyrim on a PS Vita has appeared online. The player is using the Vita's RemotePlay client to play the PS3 version of the game through the Vita console.
According to the video description, the game is being played through the Skyrim SDK, running at 26-33 fps at "95 percent" quality. Though the game may look quite smooth, the gameplay still needs a little work: "You can see how it runs, but a control scheme needs to be figured out as the mouse control stick does not move the view in realtime."
The RemotePlay feature, which allows players who own a PS3 and a PS Vita to play home console games on their handheld device, has not been released yet. Sony has shown PS3 games running on Vita using RemotePlay, but has not indicated when the feature will be released to the public.