Would there be any problems in copying files on my Linux system with ext4 filesystem to an external drive that is formatted in NTFS? I'm reinstalling my OS and intend to copy these files back to my Linux system once the new Linux OS is up and running.
No, with ntfs-3g you've got read- and write-support for NTFS formated partitions. Just additionally avoid the following characters: \ : * ? " < > |
You will maybe loose the permissions... If this is important for you (which I doubt), you have to create a tar-file first and then transfer it to the NTFS-drive.
If you are free to choose the file system of the external drive (for a further usage) I would recommend to use ext3/4 because it's more error-resistant (full journaling, fragmentation, file-system checks,...) than the NTFS-filesystem.
Permissions are what's likely to cause you the biggest headache. I've had some problems with links as well, but I tend to avoid such things on external drives.
As some of the comments point out, NTFS can be somewhat tricky as a storage filesystem when the permissions were originally from Unix.
This is a great article as to why there are such pitfalls that at first don't seem readily apparent: https://www.tuxera.com/community/ntfs-3g-advanced/ownership-and-permissions/