Overcoats and Inverness capes are probably great for normal stuff, but honestly, I wouldn't want to lug those around for hiking, which is what the OP was doing. That's a huge burden for a hiker.

If it were me, I'd invest in a lightweight poncho or rain jacket (something like this) that can be rolled up and carried in a small pouch or rucksack. Hiking in the woods isn't really the place where one need be concerned with being authentic to Highland tradition, especially if it's going to weigh you down and make the rest of your hike less pleasant.

Most ponchos are long enough to cover a kilt, and you can find jackets like the one I linked to above that will be long enough too. The advantage to a poncho, too, is that it can cover a backpack if you're wearing one. And many can double as an emergency shelter.

Hikers should always carry a minimal amount of emergency gear that's relevant to their environment. If torrential rain is a regular occurrence in your area (oh how I envy you!), then you should probably make a light but effective piece of rain gear part of your standard load-out... even if you're only going out for an hour or two.