Anybody selling edible food needs a license to do that. Moreover, you are doing a hot dog stand in the public and you probably need another license for that.
You must check this out at the local level in order to get precise information.
It is likely that you will need -
A) A business license - just as you would with any business
B) A mobile vendors permit - to operate in a public place. This is usually issued by local police, park authorities or other local officials.
C) To comply with local board of health requirements.