Possibility 1: Underexposure due to snow fooling your camera's metering. Maybe the image is not blurry, but it is just too dim. You need to over expose by 1.5 to even 2 stops, using exposure compensation, if you are shooting snow. This is because the camera's meter tries to make the white snow gray. If this is happening, your subject will be too dim/dark.
Possibility 2: Shutter is too slow because you ARE compensating. If you have the camera set to "snow", or if you are using the + exposure compensation, the camera may be slowing the shutter quite a lot in order to over expose the meter by 1 or 2 stops as described above. That is great, BUT you still have to watch your shutter speed when at maximum zoom or you get camera shake blur. Your camera gives (I think) the equivalent of a 1,200mm telephoto lens. Rule of thumb is you'd need a 1/1,200 shutter speed to avoid camera shake at 1,200mm telephoto. Your image stabilization may let you shoot at half that speed, or maybe a bit better, but you still probably need like 1/500th of a second or faster to pull off a good shot.
Also, you need to shoot with good DSLR-type form if you are at that high a zoom. Shoot with the camera steady at your eye and elbow braced up against your body, not out at arms length using the LCD screen, or you won't be holding it steady enough. Or try using a tripod or a solid surface or something.
Do either of these sound like the problem?
Scott
Canon 5d mk 4, Canon 6D, EF 70-200mm L f/2.8 IS mk2; EF 16-35 f/2.8 L mk. III; Sigma 35mm f/1.4 "Art" EF 100mm f/2.8L Macro; EF 85mm f/1.8; EF 1.4x extender mk. 3; EF 24-105 f/4 L; EF-S 17-55mm f/2.8 IS; 3x Phottix Mitros+ speedlites
Why do so many people say "FER-tographer"? Do they take "fertographs"?
