It turns out that it's hard.
Here's the route I did.
I'm riding a pretty decent, though not amazing, mountain bike I got used for ~$300. It was a good deal, it's got relatively aggressive tires though not sand tires, disk brakes, and a shock fork. I probably need to replace the seat-post and seat because this one doesn't allow me to slide the seat back, but that's pretty minor.
Up until the far (northbound) segment of the loop it was on pavement and everything was fine. In fact it seemed like this bike seemed had WAY too much tire for what I was doing, something I'm okay with but it did seem a little silly. Then I hit the dirt. I've ridden a lot of dirt, often on a cyclocross bike with slicks. What I wasn't ready for was wet sand. It turns out that all the dirt roads here are packed sand. It's currently mud season so this makes everything *wet* sand. My little rid turned way more exciting than I had intended.
It was worth it though. A beautiful ride with amazing views including glimpses of the White Mountains off to the east,
as well as a small protected set of hills off to the west.
My biggest mistake was not bringing food. I bonked bad up on mosquitoville road and by the time I got back I had absolutely no juice left. Between that and the mud I ended up walking a number of segments.
I ran into a guy walking his dog who just said "That must be a LOT of work!" as I rode by... indeed, at the time I was on flat ground and in second gear fighting along though the wet sand.
So, next time food, and I need to get in better shape! If I do this regularly though, I think large sand-tires are in order as well.