When riding at a lesson barn, especially as a beginner, you (the student) do not get to chose your horse for the lessons. The qualified instructor will do that. I am not sure if you have visiting this particular barn before, or?? Either way, simply because there is a friesian on the property does in no way mean that you will get to ride the horse - the horse could belong to a boarder, or perhaps the trainer's personal horse, or possibly the horse is retired and no longer ridden. Around here, there are a couple friesian breeders, but those are not lesson barns. Lesson barns around here will generally have a mix of breeds (no friesians).
Whether or not a horse is a good mount for a beginner is all in the training and the horse's temperment to begin with. I own a medium pony mare, a handful of people assume that since she is a pony she must be good for kids - NOT the case. She is quite hot and unpredictable - her "hottness" occasionally goes beyond the point of being able to channel that energy into something useful, and combined with being unpredictable, she is not a suitable mount for a beginner.
My other mare is TB. They have a bad rep for themselves among certain people (ie: read that as most people who don't know the breed personally hear "TB" and think fire breathing dragon). My mare is a saint of a horse. Quiet as they come. I stick all my beginner friends on her, and someday she will be the perfect packer for my kids. She's a moose though at 17.3h, built like a WB so she is thick. Even though she is the perfect beginner horse, at this point I won't let beginners ride her regularly as she is doing so well at the higher level shows and has potential for more, provided her rider is experienced at the upper levels, this mare has potential for much higher levels. So just because she is a docile horse, doesn't mean I'd stick lesson kids on her as part of a program. When she's older and semi-retired, sure! But not now.