If you have boys the cost is a LOT less than it is for a daughter. Boys don't tend worry about competing so the training costs are less than 1/3 that of girl. Boys don't worry about riding outfits that come with competing so there's a massive savings there . No special saddle, color coordinated tack , assorted treatments for mane and tail (oh the list seems to never end ).
The typical cost for a typical male horse owner (saying they are new to riding and horses and end up with a green horse, but have another guy around to help them pick out what they need )
(Keep in mind that this is for a guy since they don't usually don't care about shows, competing or need all the fancy things)
Training rider and horse (less than a year if they spend the time and have a good instructor), but we'll say 12-18 months since they might not be on a farm with their horse in the yard and the instructor 1/2 mile away (or they dad to teach them).
Some things it's hard to get around buying and paying the price for "horse" items (which tend to be over priced).
One good Western, military or other saddle with a tree that displaces weight well. One of the few things that should not be skimped on.
(we'll include the cinch in this purchase). No special saddle needed for a non competing child.
Train the horse to ride with a halter (one of the many pleasures of neck reining) and you can save the price of a bridle.
Have them spend 3 weeks with a trimmer and they can do their own hoof care.
Apron, hoof knife, a good rasp/file (shop and skip the horsey store) and stand should be doable for around $300 (and will pay for itself).
I suppose you could buy a halter, but you can make a good one with a few dollars worth of cord.
A lead can be made too, but they can be pretty cheap either way.
Leads make perfectly good reins if you're not showing
A bent 10 penny nail makes an acceptable hoof pick (so can an old hook knife that's become dull)
A wire brush from you local hardware store.
An old dog brush (short bristles on one side, metal mounted in rubber on the opposite side) works great for both brushing and combing.
An old US Army 100% wool blanket from the 1960's is as good a saddle blanket as you could ever want.
Don't need any additional clothing or foot gear. I suppose you should get them a helmet (at least for when they're first learning). Any certified helmet will do.
So excluding the cost of the saddle (to variable, but should be a good one that fits well) and the cost of the trainer (again, to variable) the cost of outfitting a son to have a horse should run to about $100 or considerably less depending on who much you buy vs make or find used. Of course with the daughter who competes we won't even go into the cost of going to competitions.
Shopping for where you keep a horse (again saying that you don't have the land to keep them on) doesn't have to break the bank either. If you do a self service (the kids have to work as if they had them at home) I've seen them for $90 a month for one stall that they can have full turn out from (or not). Food is another thing that should be selected with what's best for the horse in mind. You can feed a horse a good, low, NSC/WSC diet including mostly hay and grass for less than $1800 a year. With self service board that would be under $3,000 a year.
So after the initial outlay and a year of training cost it comes to $3,000 a year for son with a horse. My children's karate-do cost more per year than that (my youngest son was a bit less). With the competing daughter the extra cost never seem to end.
Of course I'm picking on the girls who compete . I'm sure there are some who don't (I personally know 2....who are not related to me ) just as I'm sure there are some boys who do compete (I just don't know any), but the VAST majority of girls do compete in form of show (dressage, jumping, etc....) and the majority of boys don't.
In those cases girls are just more expensive than boys .