Once you have collected the 3 staff parts you will need to find the ice record , which can be found in 3 locations throughout the map all within the tank station.
Locations include:
1. To the back right corner on the middle shelf.
2. On the left as you enter near the Mystery Box.
3. Directly in front as you enter the Tank Station.

Once you have got the disk you will need to pick up the Gramophone, which can be found under the Pack a Punch machine in the excavation site. Once you have the Gramophone you will next need to head to the Ice Crazy Place Tunnel/Agartha.
Next place the gramophone on the bench at the bottom of this tunnel and a portal will now form, continue through and look for the Blue pit to find the Ice Gem.
Once you have the Gem exit back through the Portal being sure to pick back up the Gramophone.

Next you will need to find the Black Disk, which can be found in 1 of 3 locations, all near the excavation site.
Locations include:
1. To the left of the excavation site sign.
2. To the left of the Pack a Punch machine in a wheelbarrow.
3. To the Right of the site on the wall of a trench.

Once you have this Black disk continue to the floor under the Pack a Punch machine and place the Gramophone on the bench near the Blue Elemental table, this will open a hidden spiral Staircase. Take this to the bottom, where you will find the 4 Elemental statues and crafting areas for each. Next simply go to the statue second from the left to craft the Staff of ice. This staff is now complete and you are free to use it, however it will swap out for the gun in your hand.

The staff shoots bolts of ice, freezing zombies just like the Winter's Howl in Call of Duty: Black Ops