Is this battery still usable and safe? It was dropped.
No, and No. I would have it recycled immediately. There is definite internal damage, and if the plate separators fail, you have a shorted cell, which may overheat.
It is not safe to have that battery around.
Agreed, better safe than sorry with this kind of stuff.
inou8it,
This is one of the worst fall induced damages I have seen. I would take that battery to a recycler ASAP. As other have pointed out, the internal plates on that cell are near short and when that occurs, high heat and possible case failure will result. If you think you can safely discharge the battery prior to handling, I would recommend that. If you can connect it to an auto headlight until the battery is dead, you will have less chance for further case damage and acid spill.
That is definitely a no-go, get rid of it. My team had an issue with a battery 5 (wow it’s 5 years already?) years ago, we noticed that one of our bateries was unnaturally warm. It started swelling at the sides, and we immediately decided this was a potential hazzard. We put it outside in a snow pile away from buildings, and by the end of the meeting it had melted a 3’ radius in the snow. This was with the old style bateries, but regardless, you don’t take chances with chemicals. Get rid of it! (recycled, of course)
Wow. That is really cool. Scary to think what would have happened if you kept it, but still cool.
Matt,
When the battery swells unchecked (like not putting it in the snow) the case seams usually come apart and the battery acid oozes out. If the temperature rises very rapidly, a far more violent case failure will occur. Regardless, the battery uses sulfuric acid. While this is somewhat diluted (typically about 30% acid) getting in your eyes nose or mouth (or other sensitive areas) will not be something you are likely to forget. If you get acid on your clothes, you may not notice a problem until after they are washed. Many fabrics will dissolve where they are touched by the acid.
In this particular case, only one cell will likely suffer from the damage, the one closest to the corner. If that cell swells internally, it may push against the plates in the next cell and cause a short there.
hmmm… How many batteries would it take to clear a Minnesota driveway in January? 
Well, you could just use a large weather-proof heating element, but then again, the runoff could seep under your drive way, lawn, foundation, etc., refreeze (and expand), and cause much harder to fix issues than snow or ice above the ground…
or maybe not: http://www.heatizon.com/
It would only be good enough to actually find the driveway under the snow. The rest is up to you!