One rein pulling works well. I think it is a bad habit for a horse to get into, overall. I will sometimes turn my horse's head to a mesquite tree, so it can stop and grab a little to eat - but I need to be the one turning their head. It is my choice, not theirs.
For the OP: Hacking alone, there is a lot to be said for an Australian style saddle. The Mickey Mouse ears on the front (poleys) are wonderful if your horse makes a sudden stop, falls forward, or tries to spin. With my eyes closed, it feels like my Bates AP saddle.
In the picture below, you can see a folded leather rein in one of the D-rings, then wrapped around the horn. My horse doesn't need it often, but it doesn't get in the way and is waiting there for the 3-4 times a year when I think it is useful.
Where the poleys go against the thigh: