I've been riding for over thirteen years. A big way people that i know lessen board and lessons is by working at the barn. I've worked at every barn I've ridden at. For kids, a lot of trainers will trade work for lessons.
For boarding, there are barns that will only charge like 100 bucks for a stall, but the catch is that you have to buy feed and shavings and things like that. Sadly, it is generally a lot cheaper to buy these things yourself but it takes a lot of time.
If you do this, there are many kids who would do the work in exchange for just riding your horse. I have done that a lot. I cleaned stalls and took care of this woman's horses and, in return, I got to ride them and take them to shows and stuff.
Sadly, the saying is true: "The best way to make money with horses is to start with more money." People will pay crazy amounts for a horse. I know a girl who picks up horses for a couple hundred at slaughter auctions and with a little work they are wonderful.
Hope that was helpful.