The admin bar search form is lacking the get_search_form filter

[Chouby]

The correction is obvious. Just add :
$form = apply_filters('get_search_form', $form);
at line 641 of wp-includes/admin-bar.php

[SergeyBiryukov]

Since that form is not returned by get_search_form() function, not sure if it's a good idea to use the same filter.

[ocean90]

get_search_form is for get_search_form() which is reserved for themes and not for the toolbar.

If you want to replace the search from you can remove the existing with

remove_action( 'admin_bar_menu', 'wp_admin_bar_search_menu', 4 );

and then add you can add your own with

add_action( 'admin_bar_menu', 'your_custom_callback_function', 4 );

[Chouby]

I understand your point, even if it's not easy for plugin programmers to modify the 3 kinds of search forms provided (searchform.php, get_search_form and the toolbar)... Thank you for your suggestion. I will look at this.