It's a common little tidbit in most fantastical magic novels to have little men and women in funny hats flinging ice cubes(albeit a little more dangerous than ice cubes but it's practically the same) at each other.
I'm not questioning their choice of projectile. If anything is shot with enough force it will cause damage, for example, an indestructible teddy bear.
Rather I would like to know what advantages a melee weapon(spear,sword, knives etc,etc,etc) that is close to the temperature of Absolute zero which is −273.15°Celsius / −459.67°Fahrenheit would have.
This is provided that my rabbits can hold the weapon properly and use it properly. Also assume that the weapon is always at the temperature of absolute zero with the help of handwavium, the pointy part, not the handle. And assume that the weapon still functions as a weapon, we can't have it breaking in the middle of a duel.
Now, regarding the weapons structure/material. I'm not sure whether this would affect the question but I'll state it anyway. I would assume most metals would shatter like glass at such temperatures so I would assume it would be made of ice or solid nitrogen or solid helium. But since its starting to sound like a stupid idea and the temperatures are already infeasible, assume that the weapon is made of unobtanium and handwavium.
What advantages would my Winterwrath wielding rabbits have on the battlefield or duels? And before I forget, it's in a medieval-esque world. Firearms are still superior and bringing a knife to a gunfight is stupid unless you run out of bullets. Oh, the rabbits don't matter much, it's just more fun to have rabbits instead of humans.