DISCLAIMER: All of the characters/custom champions that I've made belong to their own universe. What I'm merely doing is giving them a kit based off of their theme and capabilities while trying to make them fit among the other champions lore-wise.
When Caveam is in a game (working on the other maps atm), the map is divided and has 5 specific sectors. Caveam can capture any of these sectors (turning them into Frost Sectors, which grant him bonus movement speed, bonuses to his abilities, and zone control via his ultimate over that Sector.
I've always wanted a champion that literally controls a part of the map and makes it his domain. The new Skarner does that to some extent, but it's a rather simple mechanic and doesn't give the feeling of 'true dominance' on the map.
Caveam is meant to be the definition of zone control. Having only two damaging abilities, he fits well as a support, albeit one that has several tricks up his sleeve.
Frost Wall is an exceptional tool for ganks whenever Caveam is roaming or if the allied jungler is coming to the Tyrant's lane. As his trademark ability, Frost Wall has an incredible amount of uses: teamfight disruption, engaging, disengaging, cancelling enemy channels, zoning and denying enemy escapes.
Glacial Deconstruction gives Caveam additional manipulation over his Frost Walls, allowing him to dictate not only the flow of the battlefield, but the shape of the battlefield itself. Quickly constructing and deconstructing Frost Walls can assist allies in escaping from an enemy champion that is relentlessly pursuing them. Glacial Deconstruction also grants Caveam the option of quickly destroying a Frost Wall if it was placed at a location that could cause turmoil to his team.
Arctic Prison is Caveam's most powerful spell in nearly every category. The ability to completely isolate a part of the map, secure objectives, regroup for an attack, trap the enemy team, disengage, etc. This spell is invaluable and has many different uses.
Caveam's kit is meant to be unique without having his individual abilities overloaded. Having his spells being based off of control via the creation and destruction of artificial walls allows the player to have more options and a different way of mastering the Tyrant.