The only vaguely modest thing I found is the longer style of equestrian jacket but can't find anywhere that actually sells them! Maybe a more thorough google search would find you one though:
This picture looks like it was taken in a Khaleeji country, it's lovely and everything but I can't see it being worn in a western country even if by some miracle you did manage to find and buy it:
So, I decided to put together a few outfits myself, inspired by the current equestrian uniforms worn by women.
The second look is a slightly less smart version with a riding coat and black jeans. The hijab would obviously be worn underneath the hat:
The final look is a casual one, perhaps for horse riding lessons where you don't have to wear a particular uniform. It sort of resembles these equestrian-inspired looks on the runway:
I really hope this post helps Nora! I would love to start horse riding lessons as well actually so doing your request has been quite useful for me too :D