Is Skyrim playable in 3rd-person?

Yes! A simple touch of a button can switch you between first and third person. On the PC, this button is 'F'. On consoles or if you use a controller, click the right thumb stick. It's entirely plausible to play the entire game in this view if that is your preference.

It is playable in third person for the most part. Although if by "playable" you mean "practical", then I would say that a a few things are easier done in first person.

Aiming the bow can be easier to do in 1st person, as sometimes your character gets in the way of the camera.

In caves and other cramped areas, it's easier to search all the nooks and crannies for loot in first person as well.

I also enjoy the third person mode and happy to say 90% of the game can be played that way with no disadvantages.

Fighting in particular is fun in third person, and can be easier to do that way, if you want to see where you're going when trying to place power attacks.