If a RDP client is overrun with viruses and trojans is there any risk to the Terminal server? Printers are the only local resource that is shared. Connection to the server is through a Gateway. User authentication is assured (Through something like phonefactor).
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My concern would be that on an infected client someone would use a keyboard logger or something and collect the credentials and server information that was used to establish the RDP session. If a system has malware, then having a keylogger installed is a real possibility.
If you have File Sharing turned on, yes it's possible for virus to upload themselves to the terminal service
You should be good, if you're connecting strictly via RDP. The only thing that might get you is if something weird was configured to run when the connection is established. For example, if you are using the built-in Windows RDP client then you can set a program to run when the connection is made. In the off-chance that you have something detrimental to the server set up there then something bad could happen I suppose. That's somewhat of a longshot, though, I'd think.
You might also get something funky if you set the clipboard to share with local resources. And for sure don't bring local drives to the party (following Stephen Thompson's answer on file-sharing).