The resource requirements of the Horizon Client is rather low since it is only processing the transmit of changed pixels. I'd expect no more than 100MB of usage for RAM and sub 5% CPU. Hard disk space would only be consumed by logging.
As for running SQL on the server you are connecting to - this will utilize resources of the server and not of your client system.
The Horizon Client doesn't use that much in terms of bandwidth, maxing out around couple hundred Kb/s. What causes more of an issue is an unstable connection usually described as "jitter." If your network has jitter that will definitely cause a sense of slowness.
To me this sounds like an issue on the server or backing infrastructure causing the performance issues or a network issue between your system and the server.