This question regarding selling birdseed that contains wheat or barley, etc. states that if the seeds get wet, they are chametz.
The seeds in an outdoor bird-feeder in a non-desert climate certainly get wet during the year. However, when one places seeds in his feeder, it doesn't appear to be the same as feeding his pet whom he owns. To me, it seems that once he places the seeds in the feeder, it is hefker. Does the owner care if birds come or not? He doesn't own the birds in the same way as he owns a house pet.
With these ideas, can one leave the birdseed in the feeder during Pesach, or does he need to dispose of the seeds or sell the feeder?