I think the horse in the Ashwamedha was killed with knives. The Somavajapeya involves suffocating the sacrificial animal if I am not mistaken.
The Kings does Ashwamedha Yagya and after that they release that Horse, and till where the Horse goes that land is claimed by the King if anyone opposed he has to fight with the Army of the King who did Ashwamedha Yagya.
the translation of the word 'medha' is often not interpreted as sacrifice. There are words like 'purushamedha' and 'sarvamedha'. Sarvamedha definitely doesn't mean sacrificing everyone.
Please see the second answer of this question, which is very correct and it related directly to Dharm.
You can take a look at this link on Google Books.