If you are completing the entire trail, no preposition is necessary for most verbs related to travel or transportation. The route or journey is used as an adverb, indicating the place where the travel is occurring. This is common with named routes—
— but you can also use it with arbitrarily defined trips—
- I was biking the five miles from Westwood to Santa Monica every morning.
- They drove the long way home, to take in the view.
- He rode the seven stops from Hartsfield to Five Points without incident.
If you are not hiking the entire path, however, I would likely include a preposition such as on or along. If the path is more important than the mode of transport, you can use take or follow:
- We drove on Autoroute 20 most of the way, but took the Pierre Laporte Bridge just to say we'd been on it.
- The tour follows the Mormon Trail from Fort Bridger to Big Mountain.
As to whether the trail name takes the definite article, the short answer is "usually yes" when referring to a route but not when referring to a road— but as always with articles, the matter is complicated. I can't think of any U.S. hiking/equestrian/biking trail/path/track that is not referred to without the article off the top of my head, but there are always exceptions.