You would be bound by the CC & R's of the HOA which you agreed to when you purchased the property. The other response is correct, you would need a business license even if there were some statute allowing you to have it despite the CC& R's and you would be subjecting the HOA to liability. Neighbors would also likely object due to excessive traffic, noise, increased liability exposure, etc.
Disclaimer: It is impossible to evaluate a legal problem without a comprehensive legal consultation and review of all the facts and documents at issue. Consequently, this response does not constitute or establish an attorney-client relationship but is offered for general informational purposes only. Laws differ from state to state and each case turns on facts specific to the case and parties thereto, thus this answer does not constitute legal advice, and should not be relied upon as anything more than a starting point or suggestion that the questioner seek professional assistance from a practitioner in your state or county/parish, practicing in your area of law.
The rules of the HOA and by-laws are binding covenants and run with the land. Purchasers of property are bound to know the covenants running with the land at the time of purchase.
This answer is provided for informational purposes only. Actual legal advice can only be provided in an office consultation by an attorney licensed in your jurisdiction, with experience in the area of law in which your concern lies.