I'm not so great at horseriding. My wife rides but I never had until I got a few secret lessons recently so I can surprise her when I am back in the states.
1: If you don't wear soft, cotton boxers when riding in your kilt, at least put a blanket over the saddle. The leather can get sticky against your skin and it's not fun.
2: Ride American style. (Also known as western style.) It is A LOT more comfortable and natural for someone in a kilt than the traditional European style most people use here in the U.K.

There's a lot of fuss about how impractical a kilt is for riding, but I never had any issue with it whatsoever.
Mount up, stand in the stirrups and spread your kilt around a little so it doesn't get creased, sit and go.
I found it to be quite comfortable and easy.