You could intersect the terrain object with the cone object, and then permanently remove the “outside” terrain.
But what you’re asking for is something that works more like the section planes, but is a section cone instead where you decide to hide everything inside or outside the cone. (In your case you wish to hide the outside.)
SketchUp only has section planes at this time, but you might be able to use two crossed section planes that could approximate the intersections where a cone intersects the terrain. The planes would cross at the apex point of the cone. You might even be able to use the cone for inferencing when placing the section planes.
The tricky issue is that only one section plane can be active for each entities context, at a time. So one of the planes could be in the model’s global entities context, the other plane you’d need to insert inside the terrain group’s entities context. [Double-click to enter into a group or component instance context.]
The only other way I can think of is to have a scriptlet you trigger by menu, that makes a unique copy of the terrain object, and does a boolean intersect or subtract, then hides the cone and full terrain group.
Whenever you make adjustments you run the menu command which deletes the old intersect, and makes a new one.