On Hoth there are a total of 5 Datacrons, obtainable by Republic and Empire players altogether. The guide below provides information, maps and images on how to get them.
Datacron 1 - Republic and Empire
Red Matrix Shard
Codex Entry - Galactic History 66: The Jedi Covenant
Coordinates: -738, 1705
For this Datacron you will first need to purchase a Hidro-Thinner. You can buy it from the Aurek Base Cantina Vendor (Republic) or Dorn Base Cantina Vendor (Empire) and it costs 18,000 credits. Go in Highmount Rigde at the specified coordinates and you will see a small ice block. The Datacron is encased in the block so you will first have to use the Hidro-Thinner on it and only then you'll be able to collect the Datacron.
Datacron 2 - Republic and Empire
Codex Entry - Galactic History 65: An Exile on Rhen Var
Coordinates: 1039, -1242
Go to the northeastern corner of the Glacial Fissure area and at approximately 1046, - 1046 you will find the entrance of a cave. Enter the cave and cross it. At the exit turn left and go up hill. There is an ice ledge at 1204, -976 that you'll have to jump on and follow it leftwards until it ends at about 1143, -1075 (from there you should be able to see the Datacron) and jump down .
After you jump go right and up hill until you reach another cave. Enter it and at it's end you will find the Datacron.
Datacron 3 - Republic and Empire
Codex Entry - Galactic History 63: The Terentatek Hunt
Coordinates: 3144, 475
For this Datacron you will need to go in the Starship Graveyard at the southeastern exit (shown in the first image) which is the entrance to the Star of Coruscant. Once you're inside the Star of Coruscant take the elevator to the second floor (second image). On the right side of the room there are some small crates that you'll have to climb to the top. From there, jump on the ledge on the wall on your right and follow it around the corner and jump onto a large crate. There, you will have to wait for a moving crate to arrive. When it's close enough jump on it and ride it across the room where you'll have to jump onto some large crates and climb to the highest one. Now wait for the second moving crate to arrive. When it's close it will stop for a moment and you can jump on it (works best with Sprint disabled).
While standing on this crate you can see the Datacron glowing in the distance and another moving crate. Wait until your crate meets with the other one and jump on it (you can use Sprint again). When the third and final crate gets high enough, jump on the platform where the Datacron is located.
Datacron 4 - Republic and Empire
Codex Entry - Galactic History 64: The Kanz Disorders
Coordinates: 2837, -376
Go to the Starship Graveyard in the northeastern corner of the Jedi Encampment Heroic Area. There, at about 2607, - 844 you can start climbing the ice until you get above an ice bridge. Cross it and jump on the ice ledge below. Now follow the edge of the crashed starship until you get to another ice ledge. Jump on it until you get to another starship ledge. This will lead to (guess what?) another ice ledge. Follow it around while climbing until you get to the next level of the crashed starship and the Datacron will be waiting for you at the end of the path.
Datacron 5 - Republic and Empire
Codex Entry- Galactic History 67: Mandalore the Ultimate
Coordinates: 2916, -94
For this Datacron you have to complete two phases in two different areas. In the first phase you need to go in the western side of Clabburn Tundra Area and kill the Ancient Probe, a level 47 Champion. He has a pretty long patrolling path but if you look for it around -4015,24 following the border of the exhaustion zone (first image). The Ancient Probe drops a Depleted Datacron as soon as you have this in your inventory the first phase is complete. Now you'll have to get to the Coupled Recharge Station and activate it to charge the Depleted Datacron and make it usable.
For the second phase go to the Starship Graveyard at the northern entrance of the Star of Coruscant (at 2916, -94 as shown in the second image). There is a large pipe that you'll have to run up. When you get to the top of the pipe turn back and run across the ledge until you get above the Coupled Recharge Station. Now jump down on it and use it to charge the Datacron.