I very highly recommend that you get a copy of American Society of Agricultural and Biological Engineers before going any future in your endeavors for the sake of your livestock.
To answer your question, it doesn’t matter the distance as to the tripping of the GFCI device. What distance will do is cause a voltage drop which will lead to failure of the equipment which leads to shock to the animal or even death. The installation of remote panels will have no effect on voltage drop therefore they are not needed. What is needed if a calculation for voltage drop.
One thing to keep in mind is the fact that I have been in the electrical field for more than 40 years and have been raising horses all my life. I have had as many as 26 at one time and now own 6. I have tried every trick known to mankind and have always come back to the old way of filling the tanks and breaking ice by hand. Once you lose a couple of animals you will learn.