You aren't necessarily don't anything wrong...this is a limitation of photography. The tonal difference between white snow and a black dog is too great to be captured in one photo. If you expose for the dog, the snow is too bright, if you expose for the snow, the dog is too dark...and even if you expose in the middle, this is such an extreme...both might be lost.
The solution is too choose what you want and expose for that. Probably the dog.
To find an exposure that works for the dog...you will probably need to meter carefully as either a black dog or snow will throw the meter off.
Another option would be to add light to the dog, to bring it up closer to the brightness of the snow. Flash or maybe a reflector would help.