No, because if their is a bump in the road, they can slip and fall, and on a bumby road.
I would keep the divider in. It helps to keep them steady and therefore the trailer and car steady. Also, if the division is not there your horse might feel the need to turn around, which isn't good or safe
I would leave the divider in because the horse moving around and cause injury if the horse moves a lot and also the horse moving can throw the trailer off balance a bit depending on your truck.
The answer will really depend on the horse.
Some horses prefer to have the center divider so it helps them to stay stable and reassure them. On the contrary, some horses prefer to hav room to spread their legs during the trip.
Here is a video of a horse that only accept travelling with a lot of room : https://www.youtube.com/watch?v=ZdXM_KzuETY
But here again it depends on the horse!
Hope this helps :)
if she moves a lot in the trailer i would leave the divider in as it will help keep her more stable and she will be less likely to injure herself :)