There's not enough heat transfer on the tubing. *MAYBE* if the tubing was frozen in a block of ice but i think that's much more than an average bar fridge can do. My dad tried building a coil loop column with a fan circulator inside the fridge but it just didnt help much. It was for a 10 gallon aquarium with a single halide light above.
The Peltier idea, while interesting, just doesnt have the capacity to do what the OP wants to do. A greenhouse has a massive load and loss. He's not going to have enough circuits to run ALL this electrical load. A basic $3 Peltier is 100 Watts at 12 Volts. That's 8.3 Amps for ONE Peltier unit. He's probably going to need at least 25 units to maintain the temps in the greenhouse. So, how many auto battery starter/jumpers can he run in his dorm room on one circuit? And add to that - pumps, fans, etc. The chiller is a much better solution.
Nest is POO!!