I am running nginx, which I understand runs under the www-data user account.
All my wordpress related files are currently set to root root, is this normal? Or should they be set the www-data account (and group?)
I think they should be chowned to www-data:www-data. This is somewhat more secure, because if your site gets compromised, and you had a file that was owned as root, and had the executable permissions, it would be a hell of a lot easier to run a command as root, than if all the files and directories were owned by a non-privileged user.
As long as nginx runs as www-data, you shouldn't have any trouble having the files owned by the same user
a issue you may face is automatically installing plugins in the WordPress admin will require you to login via FTP/SFTP if the files aren't owned by www-data.
For best security I wold use a different user than www-data, except for the folders that I want to be writable by the application (like image upload folder). This user can be root, but it is better, if you are not the programmer, to be owned by a generic application user like