I think it depends on how well you pretend to be confident! You would have to control your body. For example, don't tense up and don't grip with your hands or legs, make your body and breathing all relaxed. Not only will your horse think you are relaxed, you can even fool your own mind into being relaxed this way!
When you're nervous, your mind gives signals to your body that tell it to tense up, speed up your heart rate etc. When your mind is relaxed, it tells your body to relax as well. But, and this is the important thing, your body can dictate your mind, just as your mind can dictate your body. It's a recognised psychological principle. If you act a certain way, you will start feeling that way too. For example, try smiling and laughing at the computer screen right now. Your mood will probably lift a little bit. Now look really angry (eyebrows down, bare teeth). You're mood will probably get a little bit angrier as well.
I do this myself in a way. I tend to be a bit nervous if I let myself. But I try to act confident, and fool my horse, myself and other people into thinking that I am confident. It does help. If I let myself get nervous, by thinking What Ifs, talking about my nerves etc, I will actually get nervous. I try to slow down my breathing and heart rate, relax my muscles, block negative thoughts out of my mind, focus on positive things, and try to feel confident that I can handle my horse, and in 'pretending' I actually make myself feel more confident.
Sorry, a bit of a ramble, but it's hard to explain.