Hit the marker with any squadmate to begin Yeti's solo mission.
You'll start this one inside his LEGION prison. Apparently, they let him keep a giant cryogun in his cell, which seems... unwise.
The first few halls are empty, but when the computer tells you that disciplinary measures have been undertaken, get ready for a fight. Nothing heavy- some staccato waves of swarmtroopers and helltroopers- just enough to get used to your weapon. Your stated objective is to hack the two terminals in this room (lit by markers). Do note that Yeti's melee attack is more integrated into his playstyle than the base heroes- he can use it both to defrost his weapon, and to smash frozen enemies (and also just hit things in general).
The next rooms are similar- prompting you to test Yeti's specials, while ostensibly searching our Legion Resources (they're found in large, flat boxes).
While you will run into some low-level commanders here, the final fight is against the prison overcomputer, PB-49.
No need to hunt him down, he'll run right for you. He's tough, but not too dangerous- just keep pouring on the icepower, and using your specials to magnify damage. When he and his two barely noticeable henchmen are down, hack into a computer in the far room to collect some disturbing info, and complete the mission.