It takes a lot more amps (at 12 volts) then what makes it to the trailer brakes to feel anything so far as an electric shock.
Next time you have your hood open put one hand on each battery terminal - feel anything? Didn't think so.
(Warning: Nerd alert!
This is correct. Dry skin has quite a bit of resistance. Now try it with your tongue!
Or stick a metal watch band on the positive terminal, while leaning your arm across the negative ground frame. Suddenly those electrons are moving! As a car battery has quite a bit of amperage compared to a household battery, you can get skin burns from the current flowing through the wrist band.
So while it's uncommon to receive shocks from 12V car batteries, it's not impossible. Now the detective work is figuring out how the current was entering the metal parts of the float that were probably involved in the shock the lady in the example observed while riding in the float.
And that's right at the battery, with your body creating a dead short across several hundred amps of battery at 12 volts.
Technically it's not a short unless electrons are moving!
Which won't be happening much with dry skin, or even that much more with moist skin, because skin is quite good protection with that kind of low-level power source. But get some crocodile clips and connect them to the battery terminals on the one hand and to a sewing needle each on the other, and stick the sewing needles just below the surface of the skin, where the body's (electrolytic) fluids can be reached with the metal. This is guaranteed to be a really bad experience.
Electricity and the body is a really interesting subject. 10-20 microamps (1 microamp is a millionth of an amp) across the heart is often enough to induce fibrillation. But even the above unpleasant experiments shouldn't cause that to happen, unless you're going to stick those sewing needles through your ribcage.
On the topic of the OP's floating issue: Drive the float a short distance like you normally would, and brake like you normally would, with a human "reporter" in the float, holding on to the breast bar. They can give you some feedback on whether it's hard to balance during braking. Float brakes are often quite savage and act so quickly that the horse has little warning and struggles to maintain its balance (even worse when standing on an angle). It can cause scrambling injuries and float sourness. When I float horses, I try to avoid braking as much as I can by coming off the accelerator way before a turn or traffic light, and letting the vehicle slow down naturally as much as possible, and engaging brakes lightly and early rather than more heavily and late in the piece. It makes a lot of difference, and the horses appreciate it.
Good luck with it! Let us know how it goes!