My horse would spook if she doesn't hear or see a bike coming, particularly from behind...........so if i heard the bike before she did then I would turn her to face the cyclist, then she'd be fine...... saying that I wouldn't ride her on the roads because she was a little unpredictable.......... on trails I could also move her right out of the way...........

Most cyclist that I encountered were considerate when passing us........ likewise I'd slow or stop if I met a horse whilst on my bike