What is the effect on humans of using dry ice and liquid nitrogen as food additives?
Nitrogen has a boiling point of 77K (-196 °C), CO2 melts at 195K (-78 °C). You don't cool down the ice cream or whatever else you want to eat to those temperatures, that would be very unsafe. Both will evaporate or sublimate quickly when they are in contact with warmer material, so there won't be much left once you eat e.g. the ice cream.

Air is composed of 78% N2 and 0.04% CO2, nitrogen gas can only be dangerous when it replaces all the oxygen in the air. Carbon dioxide is toxic at around 7-10% concentration. Both conditions are not realistically achievable by the methods you describe.

The biggest danger I see would be ingesting a piece of dry ice shortly after it was put in a drink, which would be cold enough to hurt.