@LanceOmikron  
Cherry pits like those of many other fruits, such as apples, also contain cyanide compounds. I know in apples you’d need to eat an entirely unrealistic amount to actually kill yourself though and I’d suspect it’s the same with cherries.

These are magic ponies though.
 
Horses are mostly herbivores, but as it has already been said, like most mammals they can and will eat other things under the right circumstances. Usually under stress and/or human intervention. (For further information on the latter, look up “Meat and Bone Meal”)
 
Its not just meat either. When stressed, horses may eat poisonous plants and develop a taste for them, such as bracken fern, and continue to eat them after the stressing conditions are past.

It’s true they can’t vomit, though.

Read up on it with a quick google search. The effects sound like Diabetic Keedo Acidosis in fast forward.

@SaburoDaimando  
Most mammals are omnivorous, simply leaning towards either being a carnivore or a herbivore. Very few mammals will not eat meat when under the right circumstances. Likewise many mammals typically considered carnivores will sometimes supplement their diets with vegetation.  
Humans actually require more meat than vegetation to survive. But now we eat so much artificially enriched food, it’s a moot point.

@SaburoDaimando
 
@SunnySide
 
The problem with saying that horses are omnivores because they eat meat on rare occasions is that that definition means that pretty much every animal on the planet is an omnivore. There are very few herbivores that NEVER eat meat and very few carnivores that NEVER eat plant matter.
 
So, bottom line: Horses can and do eat meat on rare occasions, but the percentage of meat consumption to plant matter consumption is far too low for them to be considered omnivores by the current standards of omnivorism.

@SunnySide  
Wait a minute. Ponies are Omnivores?

@Background Pony  
Actually, They’re omnivores with meat included. Do your research.

@LanceOmikron  
Ah. Thanks. My brain has more knowledge now.

@Potatoguy  
Some cursory research reveals that it’s actually the cherry tree’s leaves that are deadly (they produce cyanide when wilted, chewed up, etc).
 
I haven’t yet found word one way or the other about the actual cherries themselves, but I would guess that they’re harmless.

Well, it’s a cartoon, but is that real than cherries are poisonous to ponies/horses?

They commonly eat both pastry and hay/grass, why would they be unable to stomach cherries? They’re pretty much omnivores with exception of meat.