I guess with that entire scenic window shattered, and this office being high in the air where there'd almost certainly be a lot of wind, Palpatine needs a nice warm cloak.

Transcript

Palpatine: No, Anakin.
Palpatine: Enough death!
Palpatine: We can find a diplomatic solution; impose sanctions on the Jedi through the Senate if necessary.
Anakin: The Senate that is currently in open rebellion against you?
Palpatine: I am confident it is a limited movement with no real chance of success.
Anakin: And what about The Trade Federation running rampant on your homeworld?
Palpatine: This is precisely why we must be careful! Nute Gunray has a copy of the Peace Moon plans; we must prevent him from building it.
Palpatine: In the wrong hands, such a thing could be... disastrous.
Anakin: But in the right hands?
Palpatine: There are no right hands!
R2-D2: I've got the right hands!!
Obi-Wan: You've got no hands.
R2-D2: Exactly!