in a boat
A Satyr.
A goatman is a cross between a goat and a man.
Excuse Me, madame or mister, but I believe there is no 'Goat Man' in the hunger games.
she-goat
If it is a cross between a Human and a: Horse=Centaur, Fish=Mermaid, Goat=Satyr
Animals can cross a river by swimming or wading depending on the depth of the water. A bridge can be used be it man made or natural. Hikers have erected zip-line in some area for a fast and fun way to cross a river.
Step 1. Take the goat, leaving the wolf with the unappetising cabbage. Step 2. Row back. Step 3. Take the wolf. Step 4. Row back with the goat. Leaving the wolf alone. Step 5. Leave the goat and pick up the cabbage. Step 6. Leave the cabbage with the wolf and row back. Step 7. Pick up the goat, row across and continue with all three uneaten.
They crossed at low spots, took a barge down where they paid a man to cross, or tried to cross and got flooded out.
I think you're referring to the mythical half-man - half-goat creature called Pan.
Most likely the goat. A goat has sharp horns and sharp hooves that could cut a man to death if those weapons came in contact with him. However, a man with a sharp knife or a short club might be able to kill a wild goat.
A satyr
Go Across The Bridge.