The park has several trails for mountain biking, horseback riding, and walking. The red trail is for the exclusive use of hikers, and it contains all of the caches. The route looks like this:
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All 3.9 miles of the red trail is wide and well groomed. I wouldn't have many problems pushing a baby stroller across most of it. There are a few steeper hills which would make a stroller tricky, but they are easily tackled on foot. Most of the trail is relatively flat. The trail winds through several types of terrain: deep woods, along river banks, beside meadows, and close to a pond.
The trails are an easy stroll for a lazy afternoon, however if one has the time there are much nicer views to be had a half hour up into the mountains.
As for the caches, I managed to grab all 5. Icing on the cake for what turned out to be a pleasant stroll in near freezing weather.