What a beautiful property you have, Natalie!
I can see lots of issues with trying to seed that big hill- blowing in the wind, washing away with rain among them. Also, what kind of vegetation is growing there now? Seeds might not reach soil through thick vegetation, or might just be shaded too much by existing vegetation to grow if they do germinate. You might need to remove that stuff to get seeds to grow there.
Does that vegetation remain in winter? Seeding in winter might be better if no vegetation is there.
Karen