Yeah, that winter light! That's why I shoot birds with the 300/4 in winter. I'm actually contemplating getting the 200/2.8L II. A very good lens, weighs nothing, takes a TC well and can be had for no more than 750 euro.
Levina, I just love my 70-200 f/2.8 - it's my most-used lens. I'm sure the prime will be excellent and lighter. It will be a great addition to your lens collection!