Putting a fridge inside a creature is going to mess up the creature
There's nothing to really stop biology evolving a fridge. In many ways, the components are there - we've got pumps (circulatory system), radiators (consider desert dwelling animals, who have surfaces adapted for cooling), there's no cooling fluid, but prehaps an ethanol solution might work.
The problem is the chemistry. Generally, biochemistry of multi cellular organisms is adapted to quite a narrow temperature range. Most cold weather adaptions revolve around keeping the animals temperature up to a sensible level. Enzymes work slower under cold temperatures. Therefore, running your fridge will arguably slow down the functioning of your pump.
But! There's a better way!
Consider the bombardier beetle - it releases chemicals from two reservoirs that mix in a violent, heat producing reaction, that sprays boiling, corrosive chemicals over other insects
Swap out those chemicals for powerfully endothermic reactions - prehaps water and ammonium nitrate, and you have a freezing spray. Alternatively, you could have a high pressure gas reservoir, which releases nitrogen under pressure, making it cool as it does
Edit -
The water and ammonium nitrate reaction might be possible to catalyse with a fictional enzyme, which would allow it to get to a colder temperature. This would be pretty plausible with other endothermic reactions too, I think.