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Most likely cause (since you hit a deer) would be that there is a hole in the A/C Condenser (Reference Diagram) that is located in front of the radiator. This would allow the freon to escape.
As for the overheating, since some brackets were bent, etc. there is probably some damage that was done to the fan assembly not allowing the fan to function for the radiator. This would make it overheat.
Another thing that would cause both issues would be air flow restriction. If there is deer fur stuck in the condenser and blocking air flow, neither the A/C system would work properly nor would it allow air to flow through the radiator also causing the engine to overheat.