Access host's smart card reader via Remote Desktop Connection

Solution 1:

Unfortunately it is not possible.

I have a similar problem and was looking for a solution. What I found was a thread on social.technet.microsoft.com, where it says:

[...] It’s not possible. If you are connected through RDP, then your session is redirected to the client machine and will not see readers connected to the RDSH.

Solution 2:

Ensure the Smart Card checkbox within the Local Resources tab is checked and RDP should pass the authentication through from the native system to the target system, using the native system's smart card reader. I currently use this method at work.