var textAreaFormat:TextFormat = new TextFormat();
textAreaFormat.size = 30;
textAreaFormat.italic = true;

var ta:TextArea = new TextArea();
ta.x = 100;
ta.y = 100;
ta.width = 300;
ta.height = 300;
ta.setStyle("textFormat", textAreaFormat);
ta.htmlText = "This is text within a text area";
addChild(ta);

Confusing but here's the rule. TextFields can use stylesheets. TextArea or TextInput need a new TextFormat()

AS3: Adding styles to a TextArea component using new TextFormat()

ActionScript 3