You can read cookie in ActionForm via HttpServletRequest, but I don't think you can write cookie in ActionForm as I don't see a way you can obtain a HttpServletResponse in ActionForm.
You can certainly write cookie in Action Class.
My guess is you want to set a cookie if validation failed. One solution is to set a cookie bean to the HttpServletRequest object in the ActionForm. When it forward to the JSP page after validation failed, you can then write the cookie in the JSP if a cookie bean is found.