That is somewhat backwords though... Generally speaking you want it cropped in camera as close to what you want as possible so that you have the most quality you can get in the final image. As you have done here you captured alot of data that you knew you wouldnt want and then tossed all that data out the window in post. Then, you had to let your computer decide how to get you more pixels just like the camera would have done in the digital zoom. It has to add data to the image. The means that quality is in most cases going to be degraded. This is why most of us preach to get it right in camera as much as possible so that when you are doing your post work you have the most data to work with. In looking at your original, you have a little bit of the snow that is blown out but not too bad. But when looking at the curves you will notice that your shadow side is way off.
You can bring that back in and it does help a bit in the contrast of the image but the deer are still very soft so cropping in and enlarging is just not gonna work. When shooting that I would suggest that instead of backing way off. Try to zoom in as close as you can without activating the digital zoom. But then again, you are limited by your equipment and you may have been just too far away for this shot with that camera.
Scott