I have used your set up, and I will tell you you’re going to have a hard time. The biggest key here is going to be your ISO. The D750’s max ISO is 128000, but you’re going to start getting noise well before that. With the lens that you have (4-5.6) you’re going to have a hard time getting a low enough f-stop combined with an ISO that will counteract the poor light without creating noise or grain in the photos.
In an ideal world, you want to use the highest ISO your camera can give you without adding grain, combined with the lowest f-stop. On this telephoto lens, the widest f-stop is 4, which you can’t even get once you start to zoom in. Once you zoom in, your f-stop is going to be getting towards the 5.6 end. You would be able to make it work if you were photographing something still and had a tripod, because you could set a very slow shutter speed. But you can’t do that with horses, since they move.
Ideally, you would want to be able to use an f-stop of about 2.8 or wider (lower number). Again, the ISO is going to vary based on your setting, but it’s going to need to be pretty high. Use the slowest shutter speed you can without causing blur. You could try adjusting your white balance to a cooler/more blue tone. Perhaps these barns will be more well lit than your average barn.
You might see if you could rent a different lens. Either a fixed lens (around 85mm) or a 70-200 f2.8 (you can get lower on a fixed lens). If you’re going to be moving inside and outside, you could always take your camera bag and switch the lenses as you switch location.
