How to setcookie if is_page(‘page’) ? should I use add_action(‘init’) or there is another action?

template_redirect and wp (as the OP noted in comments) are good hooks to do this. But there’s a problem of logic in the sample code. I think it should be like:

add_action( 'template_redirect', 'cookie_redirect_wpse_113662' );

function cookie_redirect_wpse_113662() {
    # No cookie set, let's do it
    if( !isset( $_COOKIE['site_language'] ) )
        set_cookie_wpse_113662( 'ar' );

    # One of our pages, check/change cookie and redirect
    if( is_page( array( 'arabic', 'english' ) ) ) 
    {
        # Page is Arabic and cookie was English, change cookie
        if( is_page( 'arabic' ) && $_COOKIE['site_language'] == 'en' )
            set_cookie_wpse_113662( 'ar' );

        # Page is English and cookie was Arabic, change cookie
        elseif( is_page( 'english' ) && $_COOKIE['site_language'] == 'ar' ) 
            set_cookie_wpse_113662( 'en' );

        # Redirect 
        do_redirect_wpse_113662();
    }
});
function set_cookie_wpse_113662( $lingo ) {
    setcookie( 'site_language', $lingo, time() + 3600 * 24 * 365 * 3, "https://wordpress.stackexchange.com/", '.example.com' );
}
function do_redirect_wpse_113662( $where="" ) {
    $where = empty( $where ) ? home_url() : $where;
    wp_redirect( $where );
    exit();
}

There’s another problem, it would be better to go back to the original page when we click on the links Arabic and English: home_url() should be site_url($last_url). See this post, by Konstantin Kovshenin.

For this, at each page, the link for those pages should be http://example.com/LANGUAGE/?original_url=$last_url. But that’s a topic for another Question^*.

^{* I’ve played with the concept and did this plugin.}