WordPress : How to modify parameters of default Tag Cloud Widget

Tag Cloud Widget gives visitors ability to browse different topics based on tags on your site. Recently I wanted to customize it a little for this site and assumed the widget itself would give you these settings, but you can only edit the most basic parameters. Instead of widgets, we can display the tag using WordPress function wp_tag_cloud in the template, which supports more parameters. But what if we want to use existing cloud tag widget? Luckily, there is a filter available that allows you to do that and is the topic of this article.