Firstly, there is the question of what you mean by "instantly". I should not be surprised if one could pee frozen droplets over an Antarctic cliff, but I would have to see it to believe in hard pee pellets pattering onto one's boots.
I suspect that Jack London's "To build a fire" was drawn from life, but he referred to spit at errr... letsee.. about -60C. Spittle is generally more dilute and frothy than urine, so it falls more slowly and freezes faster.
I understand that Mythbusters demonstrated that urine did not freeze in urination at -70C, but I did not see that show myself, so I cannot comment with any cofidence.
There certainly are a lot of nonsensical claims of pee freezing in the air at -40C, but these are rightly scoffed at by people who have routinely experienced such temperatures (and lower) without even spittle freezing in its passage through the air.
For my part I reckon that it is a traveller's tale, but bear in mind that your pee does not have to freeze to cause penile frostbite, which has been documented in, if I remember correctly, the New England Journal of Medicine in the 1970s in a medical doctor doing a morning jog in snowy weather with too little insulation beneath his tracksuit.
