Protecting a stone retaining wall from water running down it
Honestly, I would imagine your walls will be just fine with a little water running over them. The stone walls all over the Irish countryside have been standing for a year or two and seem to cope with the wet, cold North Sea coastal weather pretty well, and most of those aren't even set in mortar.  ;-)

What I definitely would do is consider what kind of footing the wall is built on. If there's a chance of water running down the wall and digging a trough at the base that undermines the wall, you might beef up the footing and/or build in some drainage.