Yes, it's about all I've ever wanted to do. It's not for everyone though. A degree in computer science is (or used to be, I've been out of school for a while) a lot of work, especially in math. In general I'd suggest double majoring if you can. I always wish I had double majored in CS and Latin.
The day to day aspects of writing software is very different from a CS degree. I enjoy both though. There's a lot more to CS than "computers"; CS isn't really about programming at all. But to be an excellent programmer, you'll need to understand the science of computing, somehow.
Bottom line: I'd recommend waiting to declare a major as long as possible. Take classes in various subjects you think you're interested in. Don't get in too much of a hurry if you're not sure. The first few CS classes are usually weed out classes, same as with many majors (Physics comes to mind). Slog through it. Don't drink too much.
Hope this helps.