I believe you can use the .setClassName("my_css_class") to style the SelectElement.
Add the css to your html something like this:
.styled-select select {
background: transparent;
width: 268px;
padding: 5px;
font-size: 16px;
line-height: 1;
border: 0;
border-radius: 0;
height: 34px;
}
You will also find a lot of information on styling using css.
If you're using any other GWT widget, ie a ListBox, you can use .setStyleName("my_class_name"). You can wrap a GWT ListBox to a SelectElement too and style it.
ListBox listBox = ListBox.wrap(mySelectElement);
listBox.setStyleName("my_css_class");
See here for more: https://bavotasan.com/2011/style-select-box-using-only-css/
EDIT: Some excellent examples for using css styling drop down boxes here: How to style a <select> dropdown with CSS only without JavaScript?
EDIT 2 Custom styling of a dropdown box
Styling individual items of a ListBox or dropdown box.
CSS:
.selectbox {
border: 3px;
border-radius: 5px;
padding: 4px;
background-color: #44f;
}
.optioncss {
background-color: #888;
}
HTML select item for example
<select id="selectbox" class="selectbox">
<option>Option 1</option>
<option>Option 2</option>
<option>Option 3</option>
<option>Option 4</option>
</select>
GWT client code to re-style items
ListBox select = ListBox.wrap(RootPanel.get("selectbox").getElement());
SelectElement elem = (SelectElement)select.getElement().cast();
elem.getOptions().getItem(0).setDisabled(true);
elem.getOptions().getItem(1).setClassName("optioncss")