The horse is shaking his harness bells to ask if stopping is a mistake.
This poem describes a person that is driving a horse-drawn carriage on a snowy evening through some woods.
The clue to why the horse is shaking his harness bells is in this line from the third stanza.
He gives his harness bells a shake
To ask if there is some mistake.
The horse has likely shaken his head in order to make the bells jingle. He is likely cold and does not want to stop in the woods here. It is uncommon to just stop in the woods like this. Therefore, the horse is worried about his master. Horses are very intuitive animals. They can tell when their masters are worried.
The speaker is worried because he feels like it is not his time to die. We all fear death, or at least avoid it. However, the speaker here does not feel that his time has come.
The woods are lovely, dark and deep,
But I have promises to keep,
And miles to go before I sleep,
And miles to go before I sleep.
He decides that he is going to go on with his life, and avoid the lure of the woods. He is not ready to die. When he says he has “promises to keep,” he means that he has obligations in his life that are important to him. Perhaps he has a family, or perhaps he has things that he wants to do still. Maybe he has a bucket list! Either way, he decides he has too far to go before he will “sleep,” or die.
This is a poem with deceptive simplicity. At first, it just seems to be about a man and a horse in the woods. When you look at it more closely, though, you see a lot of subtext. The key is the word "sleep." When you look at the words "sleep" and "promises" together, you realize that we are talking about death.