Get the first commit of 2012
$ git log --pretty=format:'%H' --after="2011-12-31" | tail -1
d41d8cd98f00b204e9800998ecf8427e
Count the number of commits since then (inclusive)
$ git rev-list d41d8cd98f00b204e9800998ecf8427e^..HEAD | wc -l
44555
Or put 1 and 2 together into a gorgeously cryptic one-liner!
$ git rev-list $(git log --pretty=format:'%H' --after="2011-12-31" | tail -1)^..HEAD | wc -l
44555