They build and install a motor turn key. I agree it should be a drivable car with no issues. It left their shop without any issues (that they knew of)
You asked if it had "coolant"? To them "coolant" could be straight water.
You should have checked and double checked the "coolant" before cold weather. I panic when it gets real cold and I live in the south!
I find it hard to understand how all the water came out of one freeze plug hole and you never noticed it.
If I were the builder I would not warranty it either.
Think about this as if it were not you.
Several months after a motor was put in a hot rod the guy brings it back and says a freeze plug came out. All the "coolant" leaked out and the motor overheated and he wants it repaired under warranty.
Sorry, but it's not gonna happen.