During Ice Climbers' up special (referred to as "up B" from here), the hitbox is around Nana's head, and only when she is flying upwards. Popo has no hitbox during the attack.
Because of these properties, it is quite risky to use it as a method of hitting the opponent while they are edge hogging. As you are almost guaranteed to lose Nana if you try, I highly recommend considering the side special instead in most such situations. Side B gains upwards momentum when you mash the special button during the animation, has a continuous hitbox and it can be used to go very high. However, if the opponent is not edge hogging, up B is often a far safer choice as it allows you to grab the ledge faster.
It is also fairly difficult to land a hit after an up throw using up B, as landing it is dependent on the opponent's damage and whether they affect the trajectory (DI) or not. What I see most top-level Ice Climbers players use instead is up air, as it can lead to juggles and keeps the opponent in a bad position. It is worth noting that up B's hitbox is surprisingly strong, and might lead into an early KO, though. You can slightly move Nana while doing up B, which can help with hitting the opponent.
The most common situation where up B can be considered a better attack than either up air or side B is when you are recovering, are almost directly below the ledge, the opponent is following you off-stage, is directly above you at an appropriate range, and you know that they will try to attack. Because of the invincibility and priority, up B will most likely hit them and possibly cause a stage spike, and Popo or even both Climbers will recover safely, depending on the distance.
In a nutshell, it is often better to consider other options before using up B offensively, but it has some uses.
