Hello- What is the client you are connecting from? HP ThinPro, Horizon Client running on a Windows laptop, etc? Ofox (reply above) is correct that there are different ways to share or redirect drives and devices. Most versions of the Horizon Client have options for this. You will want to look for "USB Redirection" and ensure that it is enabled. The behavior you are describing sounds like you have only enabled "Drive Redirection". There is also a similar setting/feature that needs to be enabled on the agent running on the VM(s) you are connecting to.
Please see below for more information: