I have found the following solution for your problem:

In your _config.php file, add the following line:

Object::add_extension('Newsletter', 'MyNewsletter');

Create a file called MyNewsletter.php:

<?php

class MyNewsletter extends DataObjectDecorator {
	public function extraStatics() {
		return array(
			'has_one' => array(
				'File' => 'File'
			)
		);
	}
	
	public function updateCMSFields(FieldSet $fields) {
		$fields->addFieldsToTab(
			'Root.Newsletter',
			array(
				new FileField('File', 'File') // doesn't work
			)
		);
	}
}

?>

Furthermore, you have to edit newsletter/code/Newsletter.php and modify the function getCMSFields():

function getCMSFields($controller = null) {
	// ...
	
	$this->extend('updateCMSFields', $ret);
	return $ret;
}

By now, I haven't found a way to make the FileField / FileIFrameField work. Perhaps somebody else has an idea how to solve this issue?