Based on what you stated here, a "dry" county means a limited number of licenses are issued, and there are restrictions on how the licensee may serve alcohol. Thus, it's not "dry" in the strictest sense of the term, just that the number of liquor licenses and the means to use them is tightly restricted. That the religious-based college snaps them all up does not change the fact that the county government still issues some licenses. So, there is precedent--the county does issue permits to allow some alcohol to be served.
That being said, you are not planning to be engaged in the business of serving alcohol. Unless the definition of "alcoholic beverage" in the county's statute includes the selling of ingredients/equipment for making alcoholic beverages, your LHBS should fall outside of the scope of the statute.
However, the county could find other ways to block your proposed business by refusing construction and tax permits, using zoning laws, etc. If the old boy's club doesn't want you to set up shop, they may do everything in their power to keep it from happening.
Find an Arkansas attorney who practices law in this field. You might have to search outside your community to find one, maybe to Little Rock or some other city in the state. Contact your
state's Bar Association to start.