you’ll want LEDs… since by the time you use extension cords and plug in ~4 high-output floodlights, you’re probably going to overload a circuit. Also, most of those bulbs are fragile once they’re hot, so packing up the whole shebang after use would go through a lot of bulb replacements.
You might be best served by buying LED floodlights and either attaching them to a tripod/stand, or if you work at H/J barns, make a hanger that you can drape on strategically placed-jump standards. Most of the LED floodlights aren’t on a plug, so you might need to get an electrician to hardwire a plug end.
I think the biggest challenge is that at 10K lumens, it’ll be blinding to look at, but with a portable light system, you’re not going to be able to hang the lights high enough. So, horses/riders will be dealing with having the lights shining directly into their eyes. You’ll also be creating spooky shadows.
I tried to do portable lights a few years ago, and was never able to get anything to work out. Good luck.