Yes, if you have a business, you should have a website. Period. No question. Without a doubt. But the real question is Why?
1. Your competition has a website.
2. People can search you online.
3. Great advertising.
4. Open 24/7
5. Improves credibility.
6. Appears more successful.
7. Increases chance of sponsorship.
8. Shows commitment.
9. Web address easier than phone #
10. Brand yourself.
That said, it's not enough that you just have a website. You must have a professional-looking site if you want to be taken seriously. Since most people search for information online. Your site may be the first chance you have at making a good impression on a potential student, buyer, seller, owner, sponsor, you get the idea. If your site looks like it was designed by a barrel of colorblind monkeys, your chance at making a good first impression will be lost.
There is one exception, if it looks like a DIY website, just wait. It will hurt you more than help you. Why? The outdated, clunky, I did this myself, on the cheap website. That is exactly what it says about you. That is what people see. That you are outdated and cheap. Don't be outdated and cheap. You work hard everyday. Have a website that is designed by an equine website designer. It matters.