I am not a powershell user... however it looks like there's a cmdlet to Invoke a HTTP Rest service, namely Invoke-RestMethod: https://technet.microsoft.com/en-us/library/hh849971.aspx
In fact the documentation on that page has an example of performing a POST request that's using the Splunk API to execute a Splunk search and getting results from it.
Armed with this, and the Splunk REST reference, it should be only minor modifications to the $Url and $Body arguments to then be able to modify your saved search (to schedule / unschedule it at whim): http://docs.splunk.com/Documentation/Splunk/6.4.3/RESTREF/RESTsearch#POST_saved.2Fsearches.2F.7Bname.7D_method_detail
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