With no prior coding experience, would majoring in web design or development be a wise decision?

I'd say learn on your own over a couple months and see f you like it first.

If you are looking for a place to get your feet wet, http://www.codecademy.com  has several different learning tracks in both web development and design on the coding aspects, and it is free and runs in your web browser. If you are looking more to get into site design, graphic design I would check out the courses over at udemy (http://www.udemy.com/search?q=web+design) where they actually have stuff that covers wireframing and photoshop and the like. Some courses are free, some you have to pay for, but the quality is excellent. To get help you can ask specific technical questions over at http://webmasters.stackexchange.com/ which is a great resource, although the community is a little snobby when dealing with rookies. A lot of times I find answers over on the stack exchange network just by running a quick search over there because its been asked before, but they definitely want only technical questions there not general ones.  If you have a totally noob question you'll probably get a better response here on quora. All in all it web development and design has many different facets and as other people have mentioned there are business development experts and project managers that work in the industry as well.

If you really like web stuff, start it right now. It is really a good choice. First start with basic stuff like HTML, CSS, Javascript, basic web design...Later move to server coding. Feel free to contact me if you have any questions. Besides, "have a faith with you passion"

I am a recent graduate in computer engineering, i was into the networking aspect of computing before i moved into web development, unlike you i have some coding experience, I moved into web because i fell in love with it, web development is something that you have to have the passion for because it is very tasking but pays well, I can tell you that i have gone two days without sleeping because i was trying to reverse engineer a site and code it back to the way it was. At first it doesn't really pay because it takes alot of your time and effort while spending time to learn the language behind the web, but when you become a guru, you will enjoy it.  so the first step is to develop the passion, then next start coding, start from the basics,html, css and javascript before moving into php, ruby, python then content management systems. thirdly, always try to improve on yesterday, the web  is a fast paced environment, faster than superman and flash combined, and if you do not improve on your skills, someone else will and take away the job from you. so improve on them and work very hard. Good news is that you can work from anywhere in the world, because your physical presence isn't always needed, and you won't need to always be in a suit.