This Weblinks Admin Hack will allow you to put HTML Tags in the Description area of the Weblinks Component; you will have to Check the Parameters and Click on the Group and check White List; (like you do for Content).

I'm hoping that Joomla Will add this to Joomla's Weblinks Component; till then here you go. 

Edit administrator\components\com_weblinks\config.xml add this before the last line (around line 32): </params>

        <param name="@spacer" type="spacer" default="" label="" description="" menu="hide" />
        <param name="@spacer" type="" default="" label="Filtering options" description="TIPFILTERINGOPTIONS" menu="hide" />
        <param name="filter_groups" type="usergroup" multiple="true" size="10" menu="hide"
            default="" label="Filter Groups" description="TIPFILTERGROUPS" />
        <param name="filter_type" type="radio" default="" menu="hide"
            label="Filter Type" description="TIPSFILTERTYPE">
            <option value="BL">Black List (Default)</option>
            <option value="WL">White List</option>
            <option value="NH">No HTML</option>
        </param>
        <param name="filter_tags" type="text" menu="hide"
            default="" label="Filter Tags" description="TIPSFILTERTAGS" />
        <param name="filter_attritbutes" type="text" menu="hide"
            default="" label="Filter Attributes" description="TIPSFILTERATTRIBUTES" />
 

 Edit administrator\components\com_weblinks\controller.php after line 74 ... $post   = JRequest::get('post');

        // Filter settings
        jimport('joomla.application.component.helper');
        $config = JComponentHelper::getParams('com_weblinks');
        $user   = &JFactory::getUser();
        $gid    = $user->get('gid');
        $filterGroups   = $config->get('filter_groups');
        if (is_array($filterGroups) && in_array($gid, $filterGroups) or !empty($filterGroups) && $filterGroups == $gid)
        {
            $post['description'] = JRequest::getVar('description', '', 'post', 'string', JREQUEST_ALLOWRAW);
        }
 

You can view the parameters and change who can use HTML in the weblinks description; just like the Article Content.

You can see the hack at Zen Joomla Templates