I keep my horses in my backyard and not every horse is able to handle that. The breeds that I have had that handled it the best are:
My current mare is Appendix and I LOVE her sensitive but solid sensible brain. Her Welsh pony is the most solid citizen I have ever had.
I have had two draft crosses here, the Perch/Morgan mare did way better than the Belgian/Qh but he had trust issues from his Amish upbringing.
I had two separate Conn/tb crosses, one handled it better than the other, oddly enough, the hotter one handled it better.
If I could afford to board and had more time it would be an OTTB all the way, but it is the rare tb, ime that can handle this lifestyle. My friend has one though so they are out there!