If you have a chance, setup the camera prior to stepping out the door. Even if you can't see the deer through a window if you can see an area with the same lighting that will work.
Due to circumstances similar to what you had, with varying amounts of snow (or water, or deep shade, or . . .) I tend to use spot metering and meter a known tone. In this case I would have tried to meter off the snow or the white tail. The meter will under expose this situation so I'll add 1-2/3 to 2 stops. Again, you could test this through a window. Verify exposure with your histogram, expose to the right without clipping anything on the right side of the graph.
It looks like this was close to mid day based on the shadows but there is some back lighting. This means the side of the deer your seeing is in shadow so set the white balance to shade or cloudy. In LR take the white balance and run it around some of the whites that aren't over exposed. Most of the whites will have a blue cast (higher % then the other 2 colors).
How far away were the deer? I'm guessing about 60 feet. Check out the depth of field chart: http://www.dofmaster.com/doftable.html
At this distance and f/8 your depth of field would be about 3 feet. Which nose did you focus on? If you selected the right deer then the left deer would have to be within 1.5 feet of depth to be in focus. So trade shutter speed for more aperture. With IS you may be able drop as low as 1/80 second and still not have motion blur. This depends on your stability and skill which will come with practice.
If you focus and recompose you have to keep the shutter release pressed half way which can be hard to do and even harder to realize if you slipped and re-focused. I +1 the back button focus idea. Also the Servo mode, even for stationary subjects. With narrow depths of field our natural front-to-back swaying can impact the in focus area. IS will take care of side to side motion or up and down motion but it can't correct for front to back sway. I don't think any swaying would explain the focus shift from the deer to the bushes behind them, the camera just missed somehow. In this case, if you're trying to get both faces in focus I'd focus on the shoulder or ribs of the right hand deer. It looks like that is about 1/2 way between the 2 faces. f you need to pick one to be in focus I'd usually make the front deer unless there is something more compelling about the one in back.
Not sure if these are country deer or city deer. City deer are more used to people being around. Country deer are more used to being shot at by people. I'm in the city and I've found that I can get really close to the deer. Move slowly and look away from the deer, act like you're not interested in them. I also tend to talk as I'm moving around, predators are usually very quiet while hunting. Sitting down in plain view can also help them relax.
I think the grainy look you mentioned is noise due to the 400 ISO, shade on the deer, and under exposure. It is pretty easy to deal with post processing and there are lots of tutorials about this. One tool I'm trying to learn to control noise is to use Canon DPP to read the RAW file and convert it to a TIF file. DPP does a better job of processing the RAW file and produces finer noise which is easier to correct. LR can import and work with the TIF files.
Don't worry about hardware, what you have is able to make wonderful images. The only way hardware would have helped in this case is if the lens is actually back focusing. With some cameras you can do micro focus adjustments but the 60D doesn't let you do that.
You can also setup exposure bracketing. This will take 3 photos each time with varying exposures, you set the amount of variance for each image. If you're not sure about the correct exposure this is a good way to "try it" and learn which one worked best.