This is a difficult question, and requires careful elaboration. First of all snowballs are typically inanimate soulless objects, that don't end up in hell to begin with. Hell is not a garbage dump of old toasters and TVs. It's not that you have heaps of used plastic bags there either. Hell is for animate beings with a soul -- beings who have sinned.
Now, how would a snow ball end up in this situation? It needs to have a soul for starters. To get one, it needs to have the potential to be something greater than a snow ball. Luckily for us we don't need to look far. Snowmen do have souls! And snowmen are made of snowballs. You know how a human embryo has a soul, so does snowman's. Snowball in this case is a snowman embryo, or if it's a big one, we call it a fetus.
Now, how can a fetus or an embryo commit sin? That's easy: original sin. By just being born they inherit the sins of their mothers and fathers. In the snowball's case, the parent is the kid who rolled the ball -- a sinner for certain. And here we go!
Spring comes before the snowball has grown from its embryonic stage into a full sized snowman, and it finds itself in hell.
How does it survive, you ask. Now, to the probabilities. As you already implied, hell is a hostile place for a lump of frozen water. The snowball needs to act fast. Luckily Satan loves to drink beer, and to keep the bottles cool he has multiple fridges with a freezer unit. The freezers are for his pizza rolls. The snowball needs to find one of those (p=0.5). If he wakes up on top of a hill (p=0.25), he can easily scout for a fridge-freezer combination, and roll downhill. If he's in a bottom of a fiery pit, game over man.
When he eventually finds the freezer, he needs to hide in it without raising too much suspicion. If Satan is around (p=0.01), game over. If not, problem solved until Satan needs ice in his drink.
So if you now add up the probabilities: 0.5 + 0.25 + (1 - 0.01) = 1.74. That's like 174%! It means the snowball will survive with absolute certainty, until Satan needs to mix a Mohito!