Can you make it so that the mouse cursor is hidden when inactive? It's slightly distraction when you forget to move it out of the way.
In the latest version of Freerider Recharged (sept 22nd) the mouse cursor automatically hides when flying.
(I will add that to the Classic version too when I get around to updating it).
You can temporarily hide the HUD by pressing "v" on the keyboard. I might make a more permanent solution for that later, or, perhaps, make it so that the HUD hides in the same way as the mouse as you suggested.
Came here to request the same thing, with the GUI being hidden. The elements aren't really distracting since they are static, but they generally make for a lower quality feel in my opinion. I would even consider making them part of a menu when you press escape rather than having them on screen at all times. These are just usual conventions in design. It's rather peculiar having them visible at all times.