A big part of the decision is whether or not you trust the trainer to put appropriate riders on the horse, use tack that fits properly, stick to the number of rides agreed upon, etc.
If my trainer asked to use my horse for lessons she was teaching in exchange for a discount on board, I'd probably say yes. However, I probably would say no to the other trainers at my barn who I don't know as well.
And FWIW, my barn charges an extra $20/hr to use their horses in lessons. Since that's an added fee on top of the normal lesson fee the trainer charges, I'd expect the whole $20 to be credited to my board in that situation.