Hot Dog Cart business. Selling this concession food could be one juicy business. Business Overview The biggest challenge to overcome in terms of starting a hot dog vending business is to secure a vendor's permit in your local community. However, even if you can't get one, you can still operate a hot dog cart on privately-owned property and cater to functions such as flea markets, auctions, sporting events and fairs. Currently, new hot dog vending carts are retailing in the...