var tf:TextFormat = new TextFormat();
tf.size = 25;
tf.color = "#FEFEFE";
var ti:TextInput = new TextInput();
ti.x = 100;
ti.y = 100;
ti.width = 200;
ti.height = 30;
ti.htmlText = "<p>Snippler Rocks!</p>";
ti.setStyle("textFormat", tf);
addChild(ti);

So from what I can tell, you can't style a TextArea or a TextInput component using a new StyleSheet(). Instead you need to use a new TextFormat().

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

ActionScript 3