In YUI datepicker control, if you want to disabled past date (ex. dates before some date), you need to set 'mindate' property.
You can find Alfresco usage of YUI date picker component in \tomcat\webapps\share\components\form\date-picker.js file. Somehow I could not find usage if 'mindate' in this js file. just for trail purpose, I simple set this property in 'DatePicker_onReady()' function as follow,