There's a module for that now: https://www.drupal.org/project/textarea_widget_for_text
It's nice and simple with an alter hook (as detailed on the module page) and in this answer.
So you've custom themed a search bar into your brand spanking new custom theme using my handy tutorial covering that topic (http://www.agaricdesign.com/note/theme-search-form-drupal-6)
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