Setting the appearance of my drop down button to be that of my hottrackappearance so that the button looks the same whether it's moused over or not does not seem to work. Is there some other way to accomplish this?
Well, the HotTrackAppearance probably doesn't have any property settings on it like BackColor. So using that Appearance won't do anything. The control resolves the default hot track colors internally.
You can turn off HotTracking and then set the appearance to any colors you want, though. I'm not sure it's possible to get the HotTracking colors programmatically, but if it is, it would have to be done using the ResolveAppearance method.