Partly, the answer is context. Multiple soldiers wouldn't be falling off one horse. "The soldiers are falling down from the horse" is a grammatically possible reading of the sentence, but a very unlikely one in practice.
In general, Hungarian tends to use a singular form for the item possessed, when multiple people each possess one of it. The singular ló here is another manifestation of that tendency.
Ah I see. I thought that might be the case. I would thank you for the "magyarázat", but you actually "Englishized" it for me. ;) Nagyon szépen köszönöm!
I guess it's like if you said in English "The soldiers fell off multiple horses." It's factually not wrong, but it sounds off and you might be misunderstood.
I don't see a problem: two soldiers falling off one horse. This sentence gives no number and provides a single horse, so this would be my first thought. No mass falling of an entire group, which is imho more unlikely than a single incident.
If we are talking about mutiple horses I would expect "their horses" anyway. Whatever that is then in Hungarian.