I figured I'd start this off by offering links to two very valuable papers regarding why horse slaughter must be stopped. The first is Horse Slaughter, An Unnecessary Evil by Raymond Goydon and Stephen Kindel for the Thoroughbred Retirement Foundation.
The Relationship Between Abuse to Slaughter by John Holland focuses on the strawman argument that slaughter is needed or there would be more horse abuse. It's actually quite the opposite.
Please remember, the horses most likely to go to slaughter are the young and healthy, primarily products of over breeding for PMU or "quantity over quality" breeding practices, as well as the racing industry and others considering relatively young horses to be discardable.