Moses 3

As the Lord revealed the creation to Moses, He makes clear that the spirits of all men and as a matter of fact, the spirits of all other forms of life were created before the physical creation took place.  At the end of the 6th day, with the completion of the physical creation, He said -

"THUS the heaven and the earth were finished, and all the host of them."  (Pearl of Great Price | Moses 3:1)

Which means to me that at the end of the physical creation, "all the host" was created.  We know that we were not physically created at that point, but yet we were all created.  The Lord continues to explain -

"...every plant of the field before it was in the earth, and every herb of the field before it grew. For I, the Lord God, created all things, of which I have spoken, spiritually, before they were naturally upon the face of the earth. For I, the Lord God, had not caused it to rain upon the face of the earth. And I, the Lord God, had created all the children of men; and not yet a man to till the ground; for in heaven created I them; and there was not yet flesh upon the earth, neither in the water, neither in the air..."  (Pearl of Great Price | Moses 3:5) 

Even such that -

"...all things were before created; but spiritually were they created and made according to my word."  (Pearl of Great Price | Moses 3:7)

In modern revelation we learn that -

"...the spirit and the body are the soul of man."  (Doctrine and Covenants | Section 88:15)

The Lord told Moses -

"...I, the Lord God, formed man from the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul..."  (Pearl of Great Price | Moses 3:7)

Thus the combination of spirit and body.  This also applies to all other forms of life as the Lord explained to Moses that -

"...out of the ground made I, the Lord God, to grow every tree, naturally, that is pleasant to the sight of man; and man could behold it. And it became also a living soul. For it was spiritual in the day that I created it; for it remaineth in the sphere in which I, God, created it, yea, even all things which I prepared for the use of man..." (Pearl of Great Price | Moses 3:9)

Thus all living things possess a soul...a body and spirit.