I'm a bit confused. 'paard' is a 'het' but the adjective has a final 'e' this definite article het (Het + adjective with final e + noun)
with indefinite 'een' the adjective has no final 'e' (Een + adjective without final e + noun)
Why Duo tell me that 'het oude' means the old one, and it's not correct?
In the context of this sentence 'Het oude.....' means 'The old....'. On its own, 'Het oude' means 'The old one'. In any language, context can cause that identical phrases can indeed mean different things.