The answer to the question in your thread title is almost always the Department of the Interior (not the Forest Service) but that's really not relevant. The exception is if the road was built as a Federal Aid Highway a long time ago, at which point the Feds may have actually deeded the land underneath the road to the county or state, but you probably won't be that lucky. Beyond that, the answer to your main question is that it depends. If the county has a genuine Right-of-Way for the road, then you need permission from them, but that is a necessary but perhaps not sufficient condition. Even if the Forest Service wanted to, they couldn't give you a permit because rallies are within the scope of a highway Right-of-Way. However, the Right-of-Way only applies to a certain amount of land, which may only be the disturbed surface of the road itself. So, as was mentioned, for the road blocks, etc, you might need a Forest Service permit, depending on how they view the world. But, since your permit is not for a competitive motorsports event, you're in much better shape. This is about as close the the ideal situation as you will find.
You can have problems in one of two areas. The first is that there is a legitimate disagreement as to whether the county has a valid Right-of-Way. This usually results from the County claiming that they got the Right-of-Way under RS-2477, which among many other things means the road was there before it was declared to be a National Forest. The catch is that the road had to be a legal public highway under Colorado law before it was declared to be a National Forest. Proving that can be quite difficult, which is why there tends to be disagreement. The other thing that is fairly common is that the Forest Service will sign maintenance agreements with counties, and the maintenance agreements don't provide the counties with all the same benefits as a real Right-of-Way. In both of those instances, you'll probably need permission from both parties. In my experience, that's not a worthwhile expenditure of time unless it is a really, really, nice piece of road.
The easiest way to find out might be to look at the BLM Master Title Plat for the townships that the road is in. If it's shown on the plat, that's a good sign, and it should have a reference number that'll allow you to get some more information (PM me and I'll show you how to find it). If it's not, that's not necessarily the end of the world, but now you're going to have to rely on asking people that might not understand the subtlety of why you're asking, so you might get the wrong answer. First, I'd call the county and ask them. Make sure you talk to their Right-of-Way administrator, and not the guy who schedules the maintenance of the road (you'll need to make friends with him later). Assuming you get the answer that you want to hear, I'd call the Forest's District Office and ask for the person who handles Rights-of-Way, tell them what the County told you, and make sure that they agree. If they do, you're almost golden, if not, see the paragraph above.
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John