The situation is there is a horse the party wants to get off a cliff. Could you put the horse in the bag of holding (assuming the horse doesn't break the weight limit and the mouth of the the bag stretches to fit the horse), throw it off a cliff, and be able to pull the horse out? Would the horse be alive still and would the bag be ok?
Wondrous items have the same Hardness and HP as their non-magical counterparts. So a large cloth sack has a hardness of 0 and 1 HP (2/inch, and 1 inch of cloth is really thick for a sack). That said, from Damaging Objects:
Certain weapons just can’t effectively deal damage to certain objects. For example, a bludgeoning weapon cannot be used to damage a rope.
If the bag were to fall on flat ground, there's no slashing or piercing damage, so it shouldn't take any damage. For a mundane bag the objects inside would be harmed, but this is no mundane bag...
The bag of holding opens into a nondimensional space
These spells and magic items create a tiny pocket space that does not exist in any dimension.
It does not explicitly say one way or the other that the nondimensional space is affected by interactions with the outside container. This question is ultimately up to your GM. However, given the wording from Extradimensional Spaces, it could be argued to said GM that since the horse is in a tiny pocket space and not in any dimension, it is not subject to the effects of gravity and inertia outside of the bag.
A final note, from Bag of Holding:
If a bag of holding is overloaded, or if sharp objects pierce it (from inside or outside), the bag immediately ruptures and is ruined, and all contents are lost forever.
If the bag were damaged by the fall, the horse would fall into the void and be lost forever. All I can say to that is I don't recommend trying this with a horse you like.
WeirdFrog has it, inertia isn't going to cross an extra-dimensional boundary, so you would NOT end up with a splattered horse when you opened the bag. I don't think the inside of the bag (which remember has zero connection or correlation with the outside of the bag) would even change orientations during the fall.
Think of it this way, the inside is like a room, completely disconnected from what goes on outside the bag. The magic item allows you to form a connection between the two. While that connection is open, I probably would allow interactions between the two.
In other words put the horse in and leave the bag open and throw it and the results might get messy.
I agree with other answers that the horse probably doesn't experience the fall, nor does the bag take any damage from the fall or otherwise increase in weight from containing the horse. However, one thing that hasn't been mentioned is this:
If living creatures are placed within the bag, they can survive for up to 10 minutes, after which time they suffocate.
So the horse could suffocate, depending on how quickly the party gets to the bag and releases the horse.