Windows cannot natively use vector files for icons, it's just that from Vista onwards the maximum icon size was increased to 256x256 and even now not all third party developers have caught up.
Programs store several versions of their icon in a resource file which resides either in the exe or a dll. If a high resolution version is not available then Windows may not attempt to scale it up to full size. That is why Putty has a small icon and Skype does not.
See here for details about finding large versions of icons.
You could however use a vectorisation program to create a vector version of an existing icon so that you can scale it up and save it at a higher resolution.