The new Twitter widget works by inserting an <iframe>
into your document. Because of this, you can't modify the style with CSS in the parent document due to Same Origin Policy.
The only changes you can make to it are the settings that Twitter expose through data-*
attributes. For example
data-chrome="noheader nofooter" data-link-color="#cc0000"
There is no option to hide the body, you can only hide the header or footer.
Documentation
The old Twitter widget worked differently, it inserted elements directly into the current document instead of an iframe, and so the old one allowed you to override styles.
If the Twitter widget isn't flexible enough for what you want then you can always use the Twitter API to obtain the tweets and essentially produce your own widget. The downside to this is you will have to manage the API calls to get the tweets and implement caching etc.