Instead of a longer article, I went for one article per structure.
Here are the others:

Hoof Wall
Sole
White Line
Bars
Heels & Heel Bulbs
Coronary Band & Periople Skin

FROG

The frog, comparatively to the other external structures, is a softer, suppler part. It should, nonetheless, be large, thick and give the feel of sturdy tanned leather. It is a sensitive apparatus, but it should never be as sensitive that the horse pulls his / her leg away when touching the frog or sulci (grooves on either side and in the middle of the frog) with a hoof pick or wire brush.

By its shape, texture and place in the foot, it allows the back of the hoof to distort medially/laterally (left/right axle): the heels can move independently. Proper, improper or lack of stimulation will directly impact the development of the back of the foot and what’s inside (digital cushion). It also plays important roles: in protecting the sensitive parts of the back of the hoof; it provides great traction action; it is critical for blood circulation and shock absorption.
It shares impact management together with the heels.

COLLATERAL GROOVES

They are the seams between sole and frog and are great indicators. By measuring their depth at the widest part of the frog, it allows you to determine the heels’ hight.

They also give other information:

This angle in the collateral grooves indicates that P3 is pushing down on the sole: beginning of laminitis.