Most homemade trailers are converted cargo trailers, which are not designed for the type of load that horses are. Horses are top-heavy, "live" weight, meaning they move and shift weight. Smaller vehicles can't handle towing a trailer with that kind of weight; my thought is you shouldn't be towing horse trailers, even custom ones, with a truck that can't handle a full sized horse trailer. Ie no Subaru's, sorry. Also, most homemade trailers don't have the support from the floor that they need to be carrying 50lbs in 4 square inches (hoof).
As far as trucks/minivans hauling horses INSIDE, they are safer IN GENERAL than a small "amature" homemade trailer. The biggest safety hazards are 1) the driver being distracted and 2) in an accident, the horse becoming a missile and injuring itself or the passangers in the vehicle. You can bet the police will not be all that forgiving to find a horse riding in the front seat to be the cause of an accident. You eliminate both of those hazards by hauling a trailer. And both of those hazards are HUGE concerns... I'm quite surprised nobody else has mentioned them. Yes, I've hauled my pony in my F150, but I tried my darndest to eliminate those two problems as best I could. I fixed about 50% of the first issue and all of the second issue by giving the horse just enough room, basically a standing stall. He could not go flying and could not break past the seat's cargo capacity and defenses. By tying him on the passanger side his head was not able to distract the driver, but it is very hard to overcome the "oh my goodness there is a horse in the back seat" syndrome. In a mini van there is nothing to stop the horse in an accident, whereas a horse trailer a) would have the ability to keep the horse contained in a glass-free enviroment with (hopefully) metal-protrusion-free areas, as well as b) eliminate the distraction factor.
Horse trailers are quite safe, if you purchase a quality rig. Many, MANY times these trailers have been in severe accidents and most of the time the horses are able to be extracted from the accident with only minor injuries. I've had friends roll over 2h trailers (wind tunnel effect... big trailer and big truck completely overcome by wind by a passing dumptruck in a tunnel) totalling both the truck and trailer, and have the horses back on the show circuit in less than a month. That's not going to happen in a minivan. In my setup in my truck, hopefully (as best as I can hope with my design) he would walk away without any significant injuries, less than in a trailer I think. But the way I did things I've never seen duplicated.
Horses really do not belong in the same compartment as people. You can "get away" with it from time to time, and with lots of planning and design you can design very good safe rigs (I've seen custom built 1 ton vans with several slant load slots in them, completely designed from the ground up to be very safe). But you aren't going to have that in your average home-job of converting your old Caravan. Like most people here, there aren't many that do more than remove seats and put in mats. Even a sheet of 1/2" plywood isn't going to do much to stop a 300lb horse. They could kick through that, never mind get thrown into it by a 50mph impact. That's not near enough! As yourself this: assume that you rear end a semi driving down the interstate. Would the horse and passangers survive? If you can honestly say yes, then go for it. But most of the descriptions of hauling setups mentioned here would not be able to say that.
As far as "not seeing the need for a full sized horse trailer" consider this... how many people do you see driving down the road with their 12' boat on a flatbed? They are cheaper than boat trailers... but boat trailers are specifically designed for the safety and ease of use for their intended purpose, transporting and launching boats. Same with horse trailers. You can buy miniature horse trailers that are made by horse trailer manufacturers that are really cute and plenty safe. There is one memeber here who always posts a picture of her's behind an F150, along with her fancy new gooseneck. Both are true horse trailers, just in miniature size. Those are far safer than a converted trailer. Horse trailers also drain urine through large cracks, which cargo trailers don't have. They have soft suspension, air holes, and lots of other horse features. I'm sure that your husband and neighbor could build a nice trailer for them, designed off of plans for a true horse trailer, but your average person wouldn't be able to do that much fabrication to make it worthwhile.
If horse trailers are so expensive locally, don't hesitate to travel. Its cheap to have a trailer shipped to you. You can get one shipped across the US for less than you pay to take delivery of a new car
Heck, I live in Louisville, 10 miles from the Ford truck plant... it still costs $900 for delivery!