There are no DateTime functions available for snippets but here is a macro that will insert the current DateTime:
Sub PrintDateTime()
If (Not IsNothing(DTE.ActiveDocument)) Then
Dim selection As TextSelection = DTE.ActiveDocument.Selection
selection.Insert(DateTime.Now.ToString())
End If
End Sub
You can open your macro explorer with Alt + F8 and create a new module and paste the code above inside the module that is generated.
Then create a new keyboard shortcut and bind it to your macro.
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