Stuart,
 
Yes, it possible.

CuteEditor shows horizontal scrolling bar only when the user input a long word (for example "Helo..................................o") and width of the long word is bigger than the width of the CuteEditor.

Anyway, if you do need to find for a solution, here it is:

1. Use the Editor.EditorWysiwygModeCss Property specifies the location of the style sheet that will be used by the editable area. Example: EditorWysiwygModeCss="example.css"

2. Put the following code into the above style sheet.

body { overflow-x: hidden; }

html[xmlns] { height: 100%; overflow: -moz-scrollbars-vertical; }