There's nothing exposed publically that would allow you to do this, but if your application will have reflection permissions, you could hack this with a CreationFilter:

public class CF : IUIElementCreationFilter
{
    public void AfterCreateChildElements(UIElement parent)
    {
        if (parent is FormattedLinkEmbeddableUIElement)
        {
            ScrollableAreaUIElement scrollElement = parent.GetDescendant(typeof(ScrollableAreaUIElement)) as ScrollableAreaUIElement;
            if (scrollElement != null)
            {
                PropertyInfo info = typeof(ScrollableAreaUIElement).GetProperty("HorizScrollbarVisible", BindingFlags.NonPublic | BindingFlags.Instance);
                if (info != null)
                    info.SetValue(scrollElement, false, null);
            }
        }
    }

    public bool BeforeCreateChildElements(UIElement parent)
    {
        return false;
    }
}

this.ultraFormattedTextEditor1.CreationFilter = new CF();

-Matt