Food is a necessity. It should NEVER be used as a training tool.
Why not? I'm presuming, which is a bad habit, that the horse is fed grass and or hay, which is it's belly filler and provides most of its needs. Missing out on a couple of hard feeds really shouldn't cause that much damage, weighed against the benefit of her thinking that the trailer is a great place to be. For some things food is a GREAT training tool
To the OP, start from a different mind frame, there is nothing difficult about teaching a horse to load. Yesterday I led my yearlings up to the trailer, on the assumption that they would happily jump in. They chose not to, but they both stood very happily looking in and smelling the straw on the floor. I was really happy with them so just led them away again.
Next step is to get the trailer actually parked somewhere that the step is as low as possible, instead of the current position where it's way high, and then just bring the guys around again.
To me the most important thing with youngsters is your belief and attitude, Is asking her to go in the trailer reasonable, yes it is.
Is it actually that much different than expecting a horse to lead quietly through a doorway into a stall or barn, no it's not.
Given that there is no reason at all why a youngster who hasn't been taught that loading is a bad thing will actually give you any trouble. Take it slow and steady, get her to follow you wherever you want to take her, and the trailer will just come naturally