Hi Dan, been a while (10 years +) since I did karate, but shiko-dachi is not a horse stance - although both are shoulder width stances. In a horse stance (kiba dachi) the feet point straight ahead, vs in shiko dachi (four point stance) the feet are turned out 45 degrees (22.5 on each side).
The differences in stances will have an impact on balance and centre.
Can you please clarify which stance you mean? Cheers