Nothing happens if you give a rose to an iron golem. Iron golems are inanimate creatures made of iron and are not programmed to interact with flowers or any other objects in a meaningful way. They are primarily designed to protect villages from hostile mobs.
While roses might be considered a symbol of love and beauty in human culture, they hold no significance to an iron golem. The golem will simply ignore the rose, as it is not programmed to recognize or respond to it.