You can create large FAT32 partitions with GParted. I did it myself up to 150-200 GiB. I hope it works for 1TB too. Be aware that the drive contains probably around 1.000.000.000.000 bytes, that means that you have to expect a partition size of 0.909 TiB.
It could be rather easily done, by deleting the existing partition and creating a new one. Please, use one of the latest GParted livecd versions.
Often, these external hard drives contain a directory with some backup software that you can install on your computer. You have to copy it in some other drive, in case you plan to use it in the future (although manufacturers usually give download links in their web pages). You can't simply convert the filesystem.
More about limitations of the FAT32 filesystem:
http://en.wikipedia.org/wiki/Comparison_of_file_systems
http://support.microsoft.com/kb/314463
(Topic moved to the Live Media support section).
*** It is highly recommended to backup any important files before doing resize/move operations. ***