That's definitely possible, although like Chiri and Squat say you better take good shoes. It can be muddy and it's quite a steep climb in places. I would advise taking the route from around Rancho Español, not El Limón village, because that route is a lot longer (for a map
Map). So if you're coming from Las Terrenas don't take the first guides you see but drive on a bit. There are paradas with tourguides everywhere along the route between Las Terrenas and Samana. They might want to persuade you to take a horse, because that means they can charge for it, but I don't see why it wouldnt be possible to get a guide to accompany you on foot. They walk themselves anyway.