The bow in the photo above (and below on the right) is a Samick SKB horsebow (sometimes also called a shortbow).
Learning how to shoot a horsebow is trickier than learning how to shoot a traditional recurve, although they have many similarities in design. There are some additional challenges, which is why I recommend that students take 3 lessons of traditional recurve before progressing to shooting horsebow, so that they have a good grounding in proper form in that style before proceeding to a more challenging style of archery.
(Same goes with anyone wanting to learn how to shoot Longbow or Olympic Recurve. Definitely study traditional recurve first, then make the transition.)
There is an issue concerning the matter of the poundages made available by the manufacturers.
Many manufacturers who make horsebows do not make low poundages: 20 lbs or less.
This phenomenon of manufacturers not making lighter poundages is not limited to horsebows either. Some manufacturers who make longbows and the higher end traditional recurves also limit what poundages they produce, knowing that their target customers are adults (and mostly men).
The Samick SKB horsebow shown above (and on the right) only comes in 25 lbs to 55 lbs (with 5 lb increments). The bow I purchased was 30 lbs, which I felt was a good poundage for my needs as an archery instructor, and knowing that most of the people wanting to learn horsebows usually have an end goal of purchasing a horsebow that is in the 30 lbs to 50 lbs range.
This consequently creates limitations on who can potentially be using the bow. Eg. Most children won't be able to pull it properly, and many people who are complete beginners really should not be using a 30 lb bow.
However someone who has done 3 archery lessons previously, and proven that they can handle 18 lbs, 20 lbs and 24 lbs, and expressed an interest in learning horsebow. Well, then we can discuss the matter as they might be capable of pulling 30 lbs.
Otherwise they will need to purchase their own equipment - which is usually the standard situation when it comes to anyone who wants to learn how to shoot horsebows (or compounds, or Olympic recurves), and archery in general as the goal of most archery students is to eventually buy their own equipment so they can practice on their own.
Someone who is petite in size will find a difficult time finding a quality horsebow that is sized correctly for them and offers a poundage they can use properly. There are a few manufacturers who make children's bows (and youth bows) that offer lighter poundages, but the issue of quality means there is a gap in the market for well designed bows that fall into these age categories. In some cases they simply don't exist, and what does exist is slim pickings.
The big name manufacturers simply aren't interested in making certain types of bows aimed at children, youth and petite adults.
Still, that doesn't mean a person cannot do archery. It just means they are limited to doing traditional recurve (or potentially longbow or compound shooting) because there are bows being manufactured and sold which are aimed at children, youth and petite adults.
The market is there in my opinion, but nobody is making them.