If you want to copy files to AWS EC2 instance...
Before you connect to the instance, wander through the tabs and find
check the box under "Local drives and resources" for your C: drive. Once
connected to the instance, open Windows Explorer and in the address
bar, type "\\tsclient\c" (without quotes). your local PC's C: drive will
(slowly) open up in Explorer and you can drag&drop.
This doesn't require any additional ports to be opened up; it goes over the RDP connection you already using for remote desktop.