if you are looking around for a horse ( I.e specifically looking to buy one), then I see no problem with your trainer going to see a horse with you. My trainer rode & watched me ride every horse we looked at when we were horse shopping. My trainer rode the horse for 10 or so minutes before I got on, to make sure that horse was safe and at my level. However, this was far from a lesson. She gave me some pointers as I rode, but that was it.
If you are seriously looking for a horse, and happen to find one that you are looking to buy, THEN you can discuss having a trial lesson with the owners approval.
If you want to ride a variety of horses, look for a barn with multiple lesson horses.
" If the entire world was one big machine, I couldn't be an extra part. I had to be here for some reason." ~ Hugo Cabret