In Settings -> Personalization -> Taskbar, enable Automatically hide the taskbar in desktop mode, and then:

(use jwno/util)
(use jw32/_uiautomation)
(use jw32/_winuser)

(def uia-com (get-in jwno/context [:uia-manager :com]))

(def taskbar-hwnd
  (with-uia [root (:GetRootElement uia-com)]
    (with-uia [condition (:CreatePropertyCondition uia-com UIA_NamePropertyId "Taskbar")]
      (with-uia [elem (:FindFirst root TreeScope_Children condition)]
        (:get_CurrentNativeWindowHandle elem)))))

# To hide it completely
(ShowWindow taskbar-hwnd SW_HIDE)

# To show it again
(ShowWindow taskbar-hwnd SW_SHOW)