You can have as many websites as you like on your server space — click here and click here for example. I guess the problem is that you can only use one domain name.
I suppose you could use a simple direct link like mine for your riding club, and use a proper domain name for your business — linking to the riding club from your business site if it is related.
The problem with free hosting is the strings attached to it — advertising usually, or bandwidth limitations. Unrelated advertising on a business website is definitely not desireable.
I don't think a paid for web-hosting service like click here will break the bank, but you never know these days!