You could just try a door sweep. They are used on the bottoms of exterior doors to seal the door to the threshold. They are adjustable up and down and they are easily cut to length if necessary. If you are not familiar this link will give you an idea of what they are.
http://amconservationgroup.com/catalog.aspx?catid=234
For a few bucks and 5 minutes it may be an easy remedy.
http://amconservationgroup.com/catalog.aspx?catid=234
For a few bucks and 5 minutes it may be an easy remedy.