The speaker in "Frost at Midnight" is awake in the night while everyone else in the house ("the inmates of my cottage") are sleeping. As the speaker enjoys the quiet and calm of this time, s/he observes the frost appearing outside and hears an owl hooting in the distance. All is peaceful - even the baby is quietly asleep in it's cradle.
We don't know why the speaker is awake - it's not windy or stormy outside. Apparently s/he is simply too involved in his/her thoughts to be able to sleep. "Abstruse" can be defined as meaning "not easy to understand." The speaker appears to be grateful to have time without the bustle of family activities in which s/he can think about the topics that don't get attention during busier times of the day.