I have seen many time whenever we try to apply css classes to the the multi line text of asp.net. It does not work.
It may happened due to the browser treat that text box as the text area. So you can do it with defining text area element in css and it will automatically apply to the multi line text box.
border:#CCCCCC 1px solid;
If still it is not working that you can set directly attributes with property such as font,font size etc.