Hi there,
elements such as the Select element are styled by the browser not by the Theme or the plugin ( ie Woocommerce ).
You have very limited styling control over them without adding a custom Javascript replacement, especially the drop down. The most we can help with is to remove the select styles ( not the dropdown ):
select {
border:none;
-webkit-appearance: none;
-moz-appearance: none;
appearance: none;
-ms-appearance: none; /* get rid of default appearance for IE8, 9 and 10*/
}
You can then apply styles to the Select box such as adding a background image for a dropdown arrow. Or you can style the TD wrapper around the select box if you need to use CSS Pseudo elements for say adding a drop down icon.