You can use treats with clicker training and not have a nipping horse but it involves training. Any and every horse starting out clicker training is going to be grabby when he/she sees treats appearing so after the horse is used to the clicker and understands the basic concept of click and treat, the first thing you want to train is not to nip and not to be grabby about treats. It's simple to do. And clicker training is not about walking around with a bunch of treats and giving your horse treats forever. It's about a journey to shape a behavior and then phase out the treats and I think that's a step lots of people never arrive at.
Also you don't have to use treats. You can use anything your horse considers a reward. I recommend before you start clicker training, you read one of Alexandra Kurland's books on clicker training horses or find a clicker trainer in your area to help get you started. Alexandra's books are especially helpful because they are full of pictures and easy to understand instructions.
I started clicker training dogs years ago, moved on to horses when I had a problem riding horse and then have just had a blast clicker training minis. It's an amazing journey so enjoy.