Removing the butterfly will not damage your motor, but I have heard that it is more difficult to start. If it was me in the situation, I wouldn't do it. It's not worth it, it adds a little bit of noise, and that isn't worth it to me. A CAI will not cause any damage either. As for starting in the cold, the other night my car sat in the driveway while it was 20 degrees outside and at 7 in the morning it was maybe 40 outside, and I didn't have a problem starting it at all. I haven't had my Injen CAI for very long, but I haven't had any problems and never heard of any problems.
My advice is to go for the CAI.