If the interaction appears unintentional (i.e. the horse accidentally steps on the snake, killing it), it might be appropriate to refer to it as an example of amensalism in that the interaction strongly negatively impacts the snake with little perceived cost or benefit to the horse. The same might apply for the crashing impact on mollusks in Cuba mentioned above. On the other hand, if horses frequently step on snakes on the off-chance that the snake could be venemous, the interaction could be beneficial to the horse. 

Look at this article also

nterspecific Killing among Mammalian Carnivores

Article in The American Naturalist 153(5):492-508 · May 1999

DOI: 10.1086/303189

There are several terms sprinkled through literature. Random killing, excessive killing, etc. Personally I follow Oksanen et al. (1985) in calling it surplus killing.

Oksanen, T., Oksanen L., Fretwell SD. 1985. Surplus killing in the hunting strategy of small predators. Am. Nat. 126:328-346.

The example you have given, of a horse killing a snke, can either be accidental or anti-predatorial behavior.

Dear Brian

I am using the term of crashing impact for invasive species over mollusk. I am preparing a paper about that assessment the mollusk crashing by horse, sheep, cow, goat, etc. in Cuba the terrestrial mollusk population of some specie is very high and common in rural areas. This type of impact never is considered

Interspecific killing is reported also without predation in carnivore guilds. Intraguild killing would the term over and beyond 'intraguild predation'.

Thanks everyone for the definitions and articles. I appreciate your time and input.

If the interaction appears unintentional (i.e. the horse accidentally steps on the snake, killing it), it might be appropriate to refer to it as an example of amensalism in that the interaction strongly negatively impacts the snake with little perceived cost or benefit to the horse. The same might apply for the crashing impact on mollusks in Cuba mentioned above. On the other hand, if horses frequently step on snakes on the off-chance that the snake could be venemous, the interaction could be beneficial to the horse.