It looks like the horse was from a hunter just beyond the bandits, I did combine those things in my mind. The amount of civil war progress required is absolutely minimal though, just going to Riverwood is usually enough to have the civil war be started in the background and the faction camps spawn.

I may be misremembering, but I think the ambush gets removed once you make any progress on the civil war, possibly even just by receiving the quest to talk to a faction recruiter. At that point, a faction camp moves in nearby and the ambush is cleared out. Speedruns steal a horse from these bandits.