I find 3/8" to 1/2" yachting cord reins (60cents a foot or thereabouts in
Home Depot, Lowes, etc.) to have a very nice feel with no problems in rein
or sun or when having to have a brief but meaningful discussion. I use
them with leather "slobber" straps. One concern might be that the rope
wouldn't break, and I doubt the "slobbers" would either, so you might want
to have a breakable snap somewhere in the loop if there would be any danger
of the horse getting caught, etc.
I prefer the feel of yachting cord to the mountain rope. Washes nicely in
machine, but don't dry in dryer unless you want it to shrink, pill and lose
some of its resiliency.