Some horses are more skittish than others; this also goes by breeding, so some types of horses are generally more skittish than others. Generally, horses bred to Go Fast OMG are more likely to Behave Badly at things that startle them, and horses bred for things like draft (pulling things behind them with more power than speed) or specialty breeds like IRL Icelandic horses, are much steadier (you will hear some of these individuals described as "bomb proof"). Riding horses could fall into either category.

The second horse might spook at unexpected noises that it might be fine with if it could see things better, particularly if it's high-strung.

The rider of the second horse is going to have to spend a little while on the trip learning their mount, and (possibly) guiding it out of Bad Habits. Which could be (for a high strung horse) shying at things, or for a super laid back horse, trying to pause to munch on convenient things.