I would agree shooting through Glass or any Filter's is not going to be a Fair test for any Lenses abilities, as for the snow, that should not cause you any problems as theres not enough detail for the AF to grab onto provided your on the bird and its not a Blizzard.
another thing I see you shot these at 500mm. and your shutter speeds were in the 1/200th to 1/320th range on the few I checked, Increasing this and trying to maintain your Lenses focal length in this case 500 mm. a 1/500th would be the lower end of where you want to be with regards to shutter speed.
Of course technique solid rest etc play heavily into this and good shots can still happen at these lower shutter speeds, but you will have to have caught the subject not moving at the point of shutter for a High IQ shot regardless of technique or rest, simply due to the bird's movement at capture...
Dan