The poem has an overall eerie feel to it, and placing the poem at night only increases the eerie and creepy feeling of the poem.
It's not uncommon for people to be afraid of the dark. My own kids refuse to sleep without a nightlight. Friends of mine like to watch scary movies in the dark because they say it makes them scarier. Scary parts of movies often happen at night because the lack of natural light disturbs people. By placing this poem at night, Walter de la Mare enhances the disturbing and ominous feel of his poem. Additionally, placing the poem at night reinforces the logical concept that somebody should be at the house where the traveler is knocking. If the poem happened during the day, it makes sense the occupants of the house might not be home. At night, the occupants should be there. If they are not there, why aren't they there? If they are there, why are they not opening the door to the man who promised to be there?
‘Tell them I came, and no one answered,
That I kept my word,’ he said.
Are they not answering because they are in a deep sleep? Are they dead? There are so many questions that a reader begins asking because the poem is taking place at night. For the mood of the poem, it simply works better at night.