<div class="sub-middle-column">
  <div class="div-header">Grandsire
    <a "#", class="table-control-focus sub-header-table-focus" id="table-control-focus-t" >abc</a>
    <ul class="table-controls hide side-action-items">
      <li>
        <a data-remote="true" data-box-no="1" class="find_or_add_horse" href="#">Find/Add Horse</a>
      </li>
      <li>
        <a href="go_to_next_horse" data-remote="true">Go to the Next Horse</a>
      </li>
    </ul>
  </div>
  <input type="text" name="search" id="search" class="search_horse">
</div>

$(document).on('click', '.find_or_add_horse', function(){
  // on clicking on find/add horse link I need the value of text field here
});

console.log($(this).parents('.sub-middle-column').find('.search_horse').val());

$(document).on('click', '.find_or_add_horse', function(){
    var value = $('#search').val();
});

$(document).on('click', '.find_or_add_horse', function(){
       alert($('#search').val());
    });

$(document).on('click', '.find_or_add_horse', function(){
       alert($(this).closest('.sub-middle-column').find('.search_horse').val());
    });

$(document).on('click', '.find_or_add_horse', function(){
     var textValue= $('#search').val();
      });

$(document).on('click', '.find_or_add_horse', function(){
   var inputtextvalue = $.trim($("#search").val());
});