"The Good-Morrow" can be found in John Donne's Songs and Sonnets which was published in 1633.  It chronicles the thoughts of a young man upon awakening next to his beloved.

In order to grasp the full meaning of the use of the word "snorted," as used in this particular writing, you need to understand the reference to the Seven Sleepers. 

Trajan Decius was a Roman emperor who was zealous in his persecution of Christians.  He went so far as to revive the "art form" of sacrifice during pagan worship.  The Catholics had a children's legend, Seven Sleepers, which told of the flight of seven children. These seven children were believers in Christ and as such were sought by Decius in order to be murdered. The children took refuge in a miraculous cave where they slept for hundreds of years.  As you can imagine, seven children soundly sleeping for such a long time would produce quite a bit of slumbering sounds, or snorting. In the poem, "snorting" is used as another word for snoring or loud sounds made while sleeping.