These devices evolved in two separate occasions, but the result was the same: once triggered, the mine explodes into a cloud of cryogenic gas that freezes nearby targets. Elliot Tercorien used his specialized cryoscience training and the cryogenic compound liquid from the Mothership Zetacryo lab to create them, while an unknown party was able to scavenge similar cryonic materials around Boston to create another version.
The cryo mine deals a single point of damage to its target, but also freezes them solid and paralyzes them for 3 seconds. Use that time to beat on them with a heavy melee weapon, or score a few headshots with firearms.
These mines can be obtained from Elliot Tercorien after releasing him from stasis and going through the Cryo Lab with him. He will pick up some cryogenic parts in the area where Beckett and Daniels are frozen which enables him to start making the mines upon return to the Engineering Core. He will give you 3 cryo grenades and 3 cryo mines after you wait an hour for him to make them. After that must wait another 3 hours for him to make 2 more each time you ask.
Behind the scenes
The cryo mine was originally a weapon cut from the final version of Fallout 3 for an unknown reason. It does not exist in the final version of the game, nor does it exist as an unused item in the G.E.C.K. editor. However, the mesh and texture are contained within Fallout 3's BSA files, these files however were not used and new meshes and textures were made to replace them in Mothership Zeta (the original mesh and texture were eventually used in Operation: Anchorage as spider drones). Another cryo weapon, the Cryolator exists only as a mesh and textures in Fallout 3's BSA files.
PCPlayStation 3Xbox 360 If you are caught in the blast and you are paralyzed, the frost effect will not appear.
PCPlayStation 3Xbox 360 After the quest "This Galaxy Aint Big Enough..." Elliot seems to lose the ability to create cryo grenades and mines for the player.
PCPlayStation 3Xbox 360 Picking up a placed cryo mine will give you a frag mine instead.
The version which was cut from the base game
↑The Lone Wanderer: "Do you think you can make use of that stuff you picked up in the Cryo Labs?" Elliot Tercorien: "Yeah, I think so. Before I was shipped out to Anchorage, I was trained in cryoscience. We were hoping to apply that to medicine. The compounds we used weren't that different from this cryogenic liquid. I'm pretty sure I can make us some improvised weapons from it. I'm thinking something along the lines of cryo grenades and cryo mines... I don't know yet. Check back with me in about an hour and I'll see what I can do." (Elliot Tercorien's dialogue)