The trail is officially open dawn until dusk, so the hours vary depending on the time of year. The Trail gates do get locked when the river floods, so expect the park to be closed if the river is in a flood stage. It is usually closed for several days past the flood event so the trails will dry. I'm a member of HMBA (Hoosier Mountain Bike Association) who maintains the park for the city. The hours are a city park rule, and the gate closure is controlled by HMBA during the flood events.
Also when it has rained alot there are parts that is flooded which make the path closed too. There is a lake that has a run off to the white river the path goes through. Well you know, when the water is high, that is flooded.
Officially 8am - 8pm daily. However recommend you check trail condition and status at hmba.org, especially if it's been raining, trail may be closed.
Thanks! Your answer is awaiting moderation.