Whether or not patrons can access the interior isn't the potential issue that concerns me. I'm concerned because:
1) The Florida statues quoted so far regarding vehicle carry have only talked about private conveyances, and an ice cream truck might not qualify, regardless of whether the OP is the owner or not.
2) The statutes allow for carry (even concealed) without a permit in a place of business, but I'm not positive that would apply when the place of business is a vehicle. Maybe it does, maybe it doesn't, but that's the point that concerns me the most.