Do I need a license to sell snow cones in Texas?

Yes. You need a local AND a State business license to do business in Texas. There are State AND Federal laws you must follow, standards you must meet, and inspection certifications you must get, before you can legally sell ANYTHING people are actually going to consume...

Legally, yes you need a license and there are all sorts of health codes you have to meet to sell any food item.

Snow cones are a food product, the sale of which would be regulated not by the state, but by the county.

Absolutely not. Do you want to go out to the end of your driveway, set up a table , and set up an ice cone making machine. You want to dump a bunch of ice cubes in front of somebody and let them watch you make an ice cone and then add whatever flavor they want and they're stupid enough to buy it, then you don't need anything but the ice cone machine and ice and Power.

You don't actually think you're going to make any money doing this to you? Anybody can make ice cones.