If it's a VFAT partition, you can indeed not change permissions. VFAT partitions have an entirely different set of file permissions than Unix filesystems. Mounting those partitions is handled specially, in that the user mounting them gets access (modified by the umask parm of the mount).
If you want write access as a user, make sure the partition is listed in /etc/fstab with the user option, and the noauto option to avoid root mounting it at boot time, and mount it as the user in question. An example fstab line is:
/dev/hda1 /mnt/windows vfat noauto,user 0 0