Windows 10 IoT is NOT Windows 10.
In IoT, you do not have a Windows Desktop and you cannot run an application like on your desktop.
The closest thing to a remote connection is Poweshell command prompt that you can access using SSH connection or Powershell remote access.
Drivers for IoT are also limited at the moment, your Serial device may or may not run, if its a FTDI chipset then most probably it will run.
End of the day, you are required to write an application that will run on the Windows IoT Pi.
It may be graphical, by using Universal Apps build by the free Communicty version of Visual Studio.
Or it may be a console, or background application written in C# that will dump data to a remote SQL server, FTP storage, dropbox, samba share, email, etc ,etc.
Windows IoT is not a desktop OS, its an embedded OS.
(It may be possible that over the years a Mini, X like or Desktop something may be created, but for today, no, you cant just remote desktop into it and install stuff. You will be able to do this with the new Lumia 950 range though, that runs a Full Windows 10 Desktop OS, with USB support, etc etc)