I wish your videos were longer and with more parts of the process, without cutting them, fast-forwarding or skipping everything... It's so good! But that would be too much to ask and I don't want to be annoying and capricious about something that is clearly difficult to do (draw and animate, sound effects and all). TAKE YOUR LIKE.
No, it doesn't cause pain. This is because hooves are essentially just really big fingernails, there's no nerve endings except for the edge (which the shoes and nails are too far to reach. The reason the heated shoe is placed first before being cooled is to brand an indent so it's easier to then attach it later. Once again, this doesn't cause any pain to the horse if done correctly (at most it'd be like touching something hot with super long nails, something mildly uncomfortable but otherwise no big deal) If the horse feels any pain at all during this, you would absolutely be able to tell, and it wouldn't be the standard procedure for hoof care anymore