You may need to remove the horseshoes from your hoof boots for a variety of reasons. Whether it be to change the shoe out for a new one (they do eventually get dinged up), try a different style of horseshoe, add grip studs to the horseshoes, or temporarily remove the shoes.
I'll temporarily remove the horseshoes from my boots when I'm wearing them indoors (to protect my floors). I wear my boots inside farily often (in addition to actual pony play scenes, I'll also simply wear them around the house to practice walking in them), so I moved away from using a screwdriver to manually remove and replace the shoes awhile back due to the added time it takes.
Originally, I used the boots completely unshod indoors, but over time, I became worried about damaging the bottoms of the boots themselves, so I started replacing the horseshoes with hoof medicine/soaking boots (e.g. Davis brand soaking boots). The soaking boots cannot accomodate a standard Reactor boot (due to the balancing bar at the back of the horseshoe) unless you cut a slit in the back of the soaking boot.
Thus, when using my boots in the house, I'll remove the shoe from the boot as in the video above, then put the unshod hoof boot into a Davis boot. The Davis boots (and other brands of medicine/soaking boots) are soft and should protect hardwood floors while also protecting the bottoms of your hoof boots.
Fortunately, it's much easier to remove horseshoes from hoof boots than from bio-horses. Most shod hoof boots have their horseshoes attached with screws (as opposed to the nails used to attach them to a bio-horse hoof). This means the shoes can be rmeoved and replaced fairly often without causing significant damage to the boots.
With an impact driver, you can remove the horseshoe from a hoof boot in a few seconds making removing and replacing the shoes a breeze. It shouldn't be a chore to temporarily pull the shoes from hoof boots so you can prance around indoors on hardwood!