He's your typical dude. You know, the one riding his horse though the countryside around 5:00pm near the end of December, taking a breather to watch the woods fill up with snow. Wait just a minute. Who is this guy? Well, for starters, he is slightly lacking in the confidence department, as the first line suggests: "Whose woods these are I think I know." Why can't he just say, "I know whose woods these are?" Instead, he has to go and invert his sentence and tell us that he thinks he knows what's going on.
Second, our speaker is one of those people who just loves nature, who can't get enough of it. He is so taken by the sight of the woods that he doesn't quite know what to do with himself and almost gives up on his village life, his home, and his family, in order to, well, we're not sure exactly what.
It's right about then (when he has to remind himself of the promises he has to keep and of the miles he has to go before he can sleep), that we get the sense that something might be awry. Perhaps, instead of being a nature lover, our speaker is philosophical and reflective. Maybe he's one of those people who is always in his head. If that's so, he may just be reflecting on something deeper and darker, like death. Perhaps it's the end of the year, people all around him are getting their New Year's resolutions ready, and he is trying to figure out what life is all about. Perhaps he's thinking, "Am I all about my life in the warm, cozy village with the warm, cozy villagers, or should I try to find more meaning and feel closer to a higher power by chilling with nature?" Either way, our speaker is a very thoughtful (and perhaps slightly depressed) guy.
Third, we wouldn't totally blame you if you began to question our speaker's sanity. He seems like a normal guy at first, one who's communicating in a poetic kind of way, but then we realize that he's trying to guess his horse's thoughts and that he kind of wants to hang out all night and look at the woods. There's something in that first line too that suggests he's not thinking normally ("Whose woods these are I think I know"), and he seems way too paranoid about getting caught trespassing on someone else's property. If it's snowing, it must be cold. If it's evening, it must be dark. If there is no farmhouse close by, there's no one to help him out or give him a place to stay. We could imagine taking a break to appreciate the scenery in the middle of the day, but it's the evening, which means that temperatures must be dropping and that the road home must be difficult to see.
Finally, yes, our speaker may be a bit strange for trying to decode his horse's thoughts, but this effort also tells us that he's a caring, empathetic kind of guy who spends a lot of time with his horse and who loves it very much. He wants to know how his horse is feeling. We get the sense that if the horse were not with him, our speaker might not make the decision to continue home right away. It's as though the horse reminds our speaker of the "promises" he has made to those in the village and reminds him of the life he has in the village.