Have you tried clicker training before?
I loooooove this method of training. And it has proven to be very effect in train so many different animals. I used it on my horse , dog and even taught my cat to sit on command using it :P
You can buy a clicker for like a dollar at pet shops or online. Then all you need is some treats.
Click the clicker then treat, do that a few times so she knows what the deal with the clicker is and how it works.
Next just have the crop on the ground or in a non threating way, make sure she sees it , but before she can react in fear , click and reward with he treat. Let her go as close as she is comfortable with, be it 3 meters ,1 or 5. Just close enough so she's not in panic mode, just repeat that a few times then try going a little closer and so on.
Once she can go right up to it move on to holding it.
Start by just touching it so she can see that if you can touch it without getting hurt it can't be that bad, then pick it up, show her, click and reward, if she wants to snif it let her if she gets frightened put it down and start over, being gentle with her the whole time.
Just working along those lines. She will soon associate the wip as a good thing that being near she gets a reward not punishment.
This is going to take a long time and alot of paitents on your behalf as it will take alot for a horse to forget somthing like this, 6 years on my Banjo is comfortable with me holding them on him, but he is still tence sometimes, altho I never ride with one on him ....but if I did games or whatever.
O and if you are worried about giving your horse treats and them getting nippy, I didnt have that problem because when you introduce the click and treat at the beggining when you reward make sure the horse isnt grabbing for it , make sure they wait till you give it to them. And once she is generally over the fear you can wean the treats off, and just use pats as the reward.