Horses differ, so there aren't any 100% rules. If Mia notices something 'scary', what works best with her is to stop for 5 seconds so she knows that I've seen it too. Then I expect her to move on. If need be, I'll bump her head a few inches to one side to remind her that I've seen it and do not care.
If I just ignore it, then she assumes I didn't see it and that I don't know it is there. And if I'm 'unaware', then she thinks it is up to her to save us both. In her defense, stops sometimes allow me to see that she noticed a dog that is 1/3 mile away, or a bicyclist.
But some of this depends on how scary something is to the horse. Mildly concerning? Ride on without stopping. Definitely scary? 5 seconds look and then move on.
REALLY SCARY OBJECTS are different. I can forget any advice about 'pushing her forward'. She can darn near canter backwards, and will. Several months ago, it was a woman walking down the road, twirling a pink parasol. Mia snorted, then shoved it in reverse and we flew backwards for about 200 yards. It was a big achievement just to keep her from spinning, but she came to a stop about 200 yards back still. In a situation like that, you can smack her repeatedly with a heavy leather strap to no avail. Been there, done that, gone backwards while whipping her rump.
Notice the leather strap around the horn:
When the horse is sufficiently afraid, or at least when Mia is, you do NOT push her forward. Period.
But I can keep her facing the threat until the threat moves away. With parasol woman, when she came within 30 yards of us, she FINALLY heard me shouting to my diarrhea-squirting horse, "It's just a F'n umbrella!" So she shut the parasol, and Mia stopped bouncing back and forth, stared, blew hard, glared at the woman...and walked on past her with a light squeeze of the calves.
Had it been an immobile really scary thing, then my best bet would have been to back up until Mia was only 'concerned' and not 'terrified', get Mia's attention on me (looking at me), then dismount and lead her slowly from the ground. [Note: do NOT try to dismount from a scared horse
who isn't paying attention to you...I did that in Jan 2009 and my back still gets sore at times from the injury that followed.] If it was scary enough, walking somewhere closer to it might be as much as I would get. In the end, her 900 lbs and 4 legs trump my 175 & 2.
That is where knowing your horse helps, and why I advocate walking them around with a lead rope for new riders. When a horse is rolling its eyes and squirting diarrhea, it isn't in the 'learn mode'. If you push that far, you have either pushed too far, or been surprised by something like a pink parasol. Pick your fights. If you fight and lose, you've gone a bunch of training steps backwards. If you have warning and know your horse, you can push their envelope of confidence without breaking it. Push them to stretch their confidence and then declare victory. You can push further later.
That is my experience with a single, very fearful horse. She is vastly calmer now, but something that seems trivial to me can still overwhelm her. At that point, my goals are A) No 'turn & burn' - keep her facing the threat instead of spinning and bolting. And B) keep her stopped, or back up until she can stop, and wait. Most of the really scary objects move. When they move away while I act calm, she figures out that a calm bsms means she can be calm too.