When the STAR Labs team was moving the imprisoned metahumans out of the Pipeline, why didn't they freeze them using Captain Cold's gun?
Why would they give Cold the opportunity to betray them?
Cold's gun is a weapon, not a cryo-stasis technology. It is designed to disable, wound and kill its targets. It would not be a suitable device for placing anyone into cryogenic stasis currently.
The CW Flash isn't immune to Cold's gun either, he simply has the ability to adjust his molecular action to resist the "freezing" affect of the weapon. He can be stunned by it and a direct hit can immobilize him, temporarily.
Even in the comics, Cold's gun never had the ability to cause gentle cryogenic states, though the Flash has been known to try and revive people using gentle molecular energies if they haven't been frozen for more than a few seconds.
Wikipedia reminds us:
Like the majority of the Flash's rogues, Snart had no innate superhuman powers. He instead relied on his cold guns and instincts. Over the years Snart had modified his weapons to allow a variety of effects such as:
A cold beam that freezes anything it hits instantly.
Creating a cold field where people and objects literally stop in their tracks. Cold uses this ability to slow down The Flash's movements.
Bathing his opponent in a wide beam of ice designed to freeze the skin of the target so they stay conscious and do not go numb to the pain. Cold used this to kill Chill Blaine who murdered Cold's sister to make him suffer as much as possible.
Creating a slippery field of ice which can slow down the Flash.
Forming sharp stalagmites on the ground to impale his enemies. Used to kill Chill Blaine after freezing the outer layer of his skin so he could inflict as much pain as possible.
An "ice grenade" which was stated to "turn this place into an iceberg". Used to freeze everything in a large radius, and the whole of Iron Heights during the events of Blackest Night.
Creating "mirages" out of extreme cold-like heat.