Hi Tyson,
Sure. The registry info I provided actually corresponds with an environment variable, so that's probably the easiest approach.
You can create a simple batch file like this (adjusting the LogFile location to your liking, obviously 
):
@echo off
setlocal
set LogFile=C:\Flex\ClientType\%username%.log
echo %DATE% %TIME%: %USERNAME% logged on to %COMPUTERNAME% with Horizon client type '%ViewClient_Type%' >> "%LogFile%"
This results in log lines like the following:
Tue 06/09/2020 22:09:39.54: testuser logged on to 2012R2 with Horizon client type 'Windows'
If you launch this from a shortcut in the Startup folder, for instance, this information will be logged whenever a user logs on.