I think we have to assume that "passing the horizon" is a subjective thing. Suppose they both can tell when they are passing their horizon. Alice blinks when she does. When Bob sees her blinking, he is passing his horizon. He infers that Alice's horizon is different from his.
I see one problem with this, though. Theoretically, it should be possible to put a fence very close to the horizon--a swarm of near-light-speed particles orbiting it. From Bob's perspective, he'd be hitting it while watching Alice hitting it at the same time.