You don't need to install splunk on every server at all.
I just run a central splunk server, and then use WMI to pull in the event logs from the servers I'm interested in.
In order to set this up you need to a) Have Splunk running on a windows machine, b) Ensure that WMI is enabled in splunk, and c) Ensure that when you installed splunk you chose to let it run using a windows account that has access to log files you're interested in on the remote machines. (phew)
Then, modify the C:\Program Files\Splunk\etc\system\local\wmi.conf file on the splunk server to pull in the info you're after.
Here's a couple of example stanzas, the first pulls in windows event log data, the second some WMI performance counters. Note, you'll obviously need to change the servernames to your servernames :)
[WMI:Application and System Event Logs]
server=SERVER1,SERVER2,SERVER3
interval = 30
event_log_file = Application, System
disabled = 0
[WMI:FreeDiskSpaceOnServers]
server=SERVER1,SERVER2,SERVER3
interval=600
wql = select Name, FreeSpace, Size from Win32_LogicalDisk Where DriveType = 3
disabled=0
Hope that helps!