In video one, a Central Park horse gets tired and/or trips.  The woman rider freaks out.

Question:  Was she over-reacting?

In video #2, the same woman sees that the horse is back in the carriage line, having returned to work.  Again, she freaks:

Question: Is the woman right to be concerned about the horse?

I'm siding with the carriage driver (who I thought was remarkably restrained).  First of all, the woman is all over Youtube complaining about the inhumane treatment of the horse, when the video clearly show that he first concern was NOT the horse, but herself.

Secondly, as one commenter put it:

As someone who grew up around horses these horses are bred to be work horses and towing these carriages really isn't bad for them. It keeps their muscles toned and keeps them healthy as they should be. he got spooked and tripped over a curb, it's not like he was hit by a car or shot. If the horse was really in pain it would be making noise, just like people do when they are in pain and it would still be on the ground.

In other words, this woman doesn't know what she was talking about.

There is nothing to suggest that this horse is weak or malnourished or had been treated badly (in fact, it looks well cared for).  Here's what happened — it got spooked and tripped.  People trip, too, but they go on with their day.