Old movie, no cars, horse draw carriages. Staring a woman who missed her carriage and had no choice but to stay in town at a large castle like mansion. The owner was a woman, who mentioned a son but he isn’t shown, but I never got the chance to finish the movie.
When you say old movie, how old it is?
Very little info, I am just wild guessing, probably not the one you are looking for, but it is one of the Google search results:
“Imitation of Life” (1959)?
According to IMDb, there is “horse drawn hearse” in the movie.