Is it possible to create a SharePoint document set via Web Services only. I have been looking into List.UpdateListItem method and Copy but could not find a way to do it. Is this even possible with Web Services only?
No, there is no native web service that allows you to create a DocSet. You have to write code to do this.
Use the client OM to create one: http://sharepointfieldnotes.blogspot.com/2010/02/how-to-create-document-set-remotely.html
Use the server OM to create one: http://sharepointfieldnotes.blogspot.com/2010/05/making-your-sharepoint-2010_31.html
Using the latter, you can wrap this call in a WCF service to create your own DocSet service and deploy it to the ISAPI folder on SharePoint. Here's the info on writing a WCF service in SharePoint: http://msdn.microsoft.com/en-us/library/ff521581.aspx