The thumbnail for the mxd created by File > Map document properties > Make Thumbnail is stored in the MXD itself. If you have file explorer open when you create/delete the thumbnail (then save the mxd) you can see the file size change.
I would be surprised if other applications could access this as it would require those applications to know the internal structure on an MXD.
The following VBA can be run from within the MXD to export it. If you place this in the normal template then you should be able to run this code in all MXD's
Public Sub ExportMXDThumbnail()
' Creates a bitmap in c:\temp of the MXD thumbnail
On Error GoTo eh
Dim pMxDocument As IMxDocument
Set pMxDocument = ThisDocument
Dim pMapDocument As IMapDocument
Set pMapDocument = pMxDocument
Dim pPicture As IPicture
Set pPicture = pmd.Thumbnail
SavePicture pPicture, "c:\temp\mythumb.bmp"
Exit Sub
eh:
MsgBox "No thumbnail to export!"
End Sub
