My 'friend' does not have any type of insurance for her horse. She rides him on the field and roads.

[SoleSource]

I was shocked tbh. Seems irresponsible to me.

It is irresponsible, unless she has thousands squirreled away to pay if there is a problem. Not sure there is much you can do about it though.

Is she a member of any body, such as a British Riding Club affiliated riding club, or the Countryside Alliance, or the BHS? As all of these offer public liability insurance to their members and any horses in their care.