You can do it with a macro that runs at startup in the ThisOutlookSession module e.g.
Code:
Private Sub Application_Startup()
Dim oFolder As Folder
Dim oItem As MailItem
Dim i As Long
Set oFolder = Session.GetDefaultFolder(olFolderInbox)
For i = oFolder.Items.Count To 1 Step -1
If TypeName(oFolder.Items(i)) = "MailItem" Then
Set oItem = oFolder.Items(i)
If oItem.UnRead = True Then
If Format(oItem.ReceivedTime, "yyyymmdd") <= Format(Date - 3, "yyyymmdd") Then
Debug.Print CStr(oItem.ReceivedTime) & vbTab & oItem.Subject
'oItem.Delete 'restore after testing
End If
End If
End If
Next i
lbl_Exit:
Set oFolder = Nothing
Exit Sub
End Sub