Question

what promise did the poet have to make?

Answer 1

The poet is probably on a mundane, routine errand and only has simple promises to keep. It appears that he lives on a farm and has driven into some little village in a horse-drawn sleigh to shop for ordinary supplies. Since it is nearly Christmas, he probably picked up some gifts for his wife and children, and the gifts for his children would be things he had promised to get them. When he got married he made the usual promises to love and to cherish, and he still intends to keep those promises, or obligations, to his wife.

Presumably he has been to the village where he does his usual shopping and is now on his way back home. If he had been on his way towards the village, he would not have stopped to look at the woods. He would not have stopped because he had too many things on his mind. But now he has accomplished his errand and his mind is free.

His little horse would not have shaken his harness to ring the harness-bells if they were on their way out, but would have shaken the bells if they were on their way home, where the horse is looking forward to being unhitched and allowed to rest in a warm barn with plenty to eat. In saying that he has promises to keep, the poet is saying, in effect, that he has responsibilities to other people and cannot indulge himself by remaining longer to look at the beautiful woods filling up with snow.

Answer 2

It signifies obligations in general. I.e, not dicking around in the woods all day.