To count the commits in a date range in your current branch do this:
git rev-list --count HEAD --since="Dec 3 2015" --before="Jan 3 2016"
If you want the count for all branches in one go use –all additionally
git rev-list --count --since="Dec 3 2015" --before="Jan 3 2016" --all
if you want to exclude merge-commits, use option –no-merges
git rev-list --count --since="Dec 3 2015" --before="Jan 3 2016" --all --no-merges