Try this it works for me,
<style>_x000D_
select{_x000D_
border: 0 !important; /*Removes border*/_x000D_
-webkit-appearance: none;_x000D_
-moz-appearance: none;_x000D_
appearance: none;_x000D_
text-overflow:'';_x000D_
text-indent: 0.01px; /* Removes default arrow from firefox*/_x000D_
text-overflow: ""; /*Removes default arrow from firefox*/_x000D_
}_x000D_
select::-ms-expand {_x000D_
display: none;_x000D_
}_x000D_
.select-wrapper_x000D_
{_x000D_
padding-left:0px;_x000D_
overflow:hidden;_x000D_
}_x000D_
</style>_x000D_
_x000D_
<div class="select-wrapper">_x000D_
<select> ... </select>_x000D_
</div>
_x000D_
You can not hide but using overflow hidden you can actually make it disappear.