Called without any parameters, the visible() method returns true if the DropDown is currently visible and false otherwise.
Calling it with a boolean true or false parameter will show and hide the DropDown widget.

<select id="ddl" ></select>

<script type="text/javascript">

    $(function () {
            dataSource: {
			    data: countries
            enabled: false,
		    textTemplate: "{name}",
		    valueTemplate: "{code}"

    $("#ddl").swidget().visible(); // return true
    $("#ddl").swidget().visible(false) // hide the widget
    $("#ddl").swidget().visible(); // return false