I would leave it and crop the right side of the frame slightly to balance the dog and the shovel within the frame. The shovel grounds the image in reality, it connects the dog to wherever you were when you took the picture.
If you take it out, you completely change the image and make it purely about the dog, disconnected from the world. There's nothing wrong with that, that too could be a fine photograph. I think you will find that you have too much dead space -- the large areas of snow will be pointless and wasteful of space -- so you will want a substantially tighter crop in this case.
With the shovel it's an environmental portrait, and lots of space around the dog is appropriate. Without it, it's just a portrait, and a closer crop is indicated. Well, traditionally. Feel free to fly in the face of tradition, as well, if you like the results.