I can't speak to the horse side of businesses, but the thing that always stopped me from filing for a business license in illinois is the requirement of paying taxes quarterly. I'm not the best at keeping up withmy paperwork, and filsing 4 times a year would not work well for me unless I was able to really focus on the business.
And it was a while a go since I looked into it, but one advantage to fileing a business license on something that most people do as a hobby is that you could actually lose money at it for six years before they say, "Hey, wait a minute, this is a hobby!"
I know that because the stables I worked for in high school was in its 4th year of losing money when they hired me. I was with them through years five and six, but after that the owner turned into a real jerk, wanting us to operate in 100 degree weather, raise prices, cut corners on expenses wherever possible, etc. (He had always been a jerk, but let the manager run everything day to day. Then he started coming around once a week and being a jerk to our faces more often.)
We didn't make money for him the sixth year, and by year eight he sold the place. (I was no longer working there.)