The Cryolator is the closest thing to Mr. Freeze's arsenal you'll find in the Commonwealth. One blast from this baby will slow your enemies down, while a couple more will shatter them like ice.
After you meet Dogmeat at the Red Rocket Gas Station just south of Sanctuary, head straight back to Vault 111. To descend back down the elevator, you'll have to press the red button in the small structure on the vault's east side. Once you've made it back down to the entrance, you should see two doorways; the right leads back to the cryochambers, and the left leads to the Overseer's office. Go through the left doorway.
In the office is a lockbox hanging on the wall with the Cryolator locked inside. No need to spot it, though! Just "talk" to Dogmeat, and ask him to "fetch" any hidden "items." He should immediately approach the lockbox and magically retrieve the gun for you.