"Previous obligations" can be described as responsibilities that a person has prior to something else coming up. Most people read the line, "But I have promises to keep," as the speaker's explanation of why he cannot remain in this lovely forest, even though he might prefer to (line 14). In saying that he has "promises to keep," the speaker makes it sound as though he has previous obligations, i.e. responsibilities or duties to which he'd committed before he was halted in his progress through the forest by its beauty and which he now feels bound to keep.
I'm not sure I would choose any of these three words -- suspenseful, peaceful, or cold -- to describe the tone of this poem. A description of tone is typically a word that describes a feeling, like indifferent, judgmental, or approving, because "tone" describes the way the author feels about the subject. Therefore, I would call the tone of this poem sympathetic. The author presents the speaker in a simple way, with a simple and perfectly relatable desire: the speaker is very tired and very busy with many responsibilities, but he stops to appreciate the beauty of the nature around him and finds that he'd prefer to rest in tranquility there for awhile. The author is clearly not judgmental of this desire. The speaker isn't complaining, and he doesn't exaggerate or whine about his duties. He presents them in an almost matter-of-fact way.
"Peaceful" could certainly be used to describe the mood of the poem. "Mood" refers to the emotional atmosphere of a text, often created by the connotations of the words and images used. Most of the words in his poem are simple and positive. Many of the words, especially, in the first stanza, are monosyllabic (meaning they only have one syllable), and this, along with the rhyme scheme and meter, help to make the poem sound steady and reliable (just like the speaker). The lovely images of the woods, the way the forest looks and sounds, also contribute to the peaceful mood.