I am involved with one of the registries (Friesian Heritage Horse) and our board members have been involved in Friesian cross breeding for over 10 years. We watch health issues closely (as well as reproduction issues), and are seeing that the crosses tend to not inherit the health issues - very much like cross breeding dogs, you get a “hybrid vigor”. The only exception is the multi-generational crosses that are 3/4 to 7/8 Friesian, where at least the reproduction weaknesses start to show up again.
This is by no means a scientific study, but it is something we are all aware of. Having said that - I’ve owned several purebred Friesians and none of them had the health issues that are so often discussed. It may be because they were always out - I have wondered if stalling them leads to higher health problems?
My crosses have been pretty hardy and healthy - I keep track of most of the youngsters I’ve sold over the years, and so far, so good. But mine are all 1/4 to 1/2 Friesian, so not a high %.
I would also point out that MOST breeds have their specific health issues. And in most cases, outcrossing helps lower the risk of those issues.
There are a few breeders that are doing Arab/Friesian crosses - I know of one who did combined driving with them and another who is showing dressage on the Arab circuit. At least for those horses, they are sound, healthy, and doing well.