The purpose of the rubber under the horse shoe is to absorb the shock from walking, troting, cantering, etc. It is exactly like the cushions people put in their shoes. If horses are going to be walking on pavement for a prolonged period of time i.e. parades, it is a good idea to have them on so it is easier on the horses. If they walk on pavement with out a rubber pad they can get quite sore in the bones and muscle. It is a really good idea to have the rubber on when going into parades.

(Also, if the hoof is too long or short, the farrier will put rubber pads on the hooves. When the hoof is too long they put it on to relieve pain, and when it is too short they use it to lengthen the hoof.

There is another kind of rubber pad (can't recall the name) used to keep foregin objects, mud, and dirt out of the hoof and frog when the horses have thrush.)

There are many different kinds of horse shoes based on the condition of the hoof, and the occasion of which the horse is being used. I've seen shoes with spikes on them to help horses get tracksion when running (horse races, polo).

Kinds of Horseshoes
The Farrier and Hoofcare Resource Center

That's really I know. I hoped that helped out any!?!