I say use the 135 L for this assignment! It is perfect for it. Trust me, the day I shot with this lens is the day I handed my 70-200f4 over, never to desire it on a camera again. AF, Sharpness, Color, Contrast, Bokeh, speed etc are all far superior on the 135L.
Yesterday it was as cold as 3deg in the morning but the afternoon it got to a comfortable 18-22deg. Today it'll be around 15deg I think.

