The choice component's button(drop down button to the right)
shows the same cursor set to choice...but in components like Textarea the scroll bar gets the DEFAULT_CURSOR irrespective of any cursor you set to these components.

In Windows:
In List and TextArea : The scroll bar gets the DEFAULT_CURSOR irrespective of any cursor you set to these components.

In Choice the cursor is same for the drop down button of the choice component.

In Solaris:
In TextArea : The scroll bar gets the DEFAULT_CURSOR irrespective of any cursor you set to these components.

In Choice the cursor is same for the drop down button of the choice component.
In List the cursor is same for the scrollbar of the List component.

You can run the following case to check this behaviour:

import java.awt.*;

public class ChoiceCursorTest extends Frame {

private Choice choice;
private TextArea textArea;
private List list;
private Panel panel;

public ChoiceCursorTest() {
panel = new Panel();

choice = new Choice();
choice.add("Choice1");
choice.add("Choice2");
choice.setCursor(new Cursor(Cursor.CROSSHAIR_CURSOR));

list = new List(2);
list.add("List1");
list.add("List2");
list.add("List3");
list.add("List4");
list.setCursor(new Cursor(Cursor.CROSSHAIR_CURSOR));


textArea = new TextArea(3,5);
textArea.setCursor(new Cursor(Cursor.CROSSHAIR_CURSOR));


panel.add(choice);
panel.add(list);
panel.add(textArea);

this.add(panel);
this.setSize(200,200);
this.setVisible(true);
}

public static void main(String[] args) {
new ChoiceCursorTest();
}
}