Stopping by the woods
The first few lines are honestly exactly what they mean.
He is obviously coming back toward his village/town after a long trip.
He does not want to press on any further because of either he is tired or because it is snowing a bit too much or for some type of normal reason.
When he talks about his horse, his horse obviously knows it is very cold out and wants to rest, but the horse realizes that they are not inside, and is wondering why they are stopping outside. Between the woods and frozen lake. That could be very literal or symbolic. It could be representative of between a rock and a hard place. Neither of the two places are really acceptible places to sleep or take a break or whatever it is he is stopping for. And the "darkest evening of the year" could be pertaining to a certain day of the year.. the winter solstice? or autumn equinox? whichever of those two that it is it may literally be referring to, or he could be dreading going back into town for some unknown reason. The "darkest" evening could be reffering to his life or a bad event that has happened recently, or is about to happen.
The horse is still concerned about stopping because of the condition of the weather, hence him giving his harness bells a shake, as though actually asking the question why are they stopping? And then he can only hear the sound of the wilderness and snowfall.
The woods are lovely dark and deep...
Many view this poem as dark, and this reffers to death, or even abandonment. That he might have a family or financial troubles that he could run away from by going into the woods, or away from everything. He mentions that he has promises to keep meaning even though it would be easier to run away, he cannot because he has commitments to attend do. Possibly a wife and children. The interpretation about death could be saying that he is an old man and he is ready to die, but he has to settle his affairs (promises to keep) before he "sleeps" (dies).
Im not very familiar with the other poem but i hope this helps