I have a 16+ hand horse, who is also very stubborn. Loading him was always a problem. What finally worked was annoying him until he just got in.
1. Start away from trailer and teach him to step forward by tapping the shaft of a short whip high on the dock of his tail. Keep tapping until he steps forward. Important to not hurt or punish him, just annoy. His reward is instantly stopping the tapping when he takes a step no matter how small. Repeat daily until his response is immediate and he will take several steps.
2. Move on to the trailer and start over again with small steps.
3. Once he loads, praise him and back out, and reload.
This method takes time and patience. Note: Whipping a stubborn horse will only make him fight. It may take 15 minutes before he will take a step. But once he learns to stop the tapping by stepping forward, you got it.