Plastic Carboy in direct contact with Ice is no problem. Glass may be an issue, but even then I would not hesitate to put my 70F glass carboy into a bath of 32F water/ice.
The only hitch I see with the carboy, is that you will want to keep the water level on the outside (after ice melting) below the water level on the inside of the carboy. That way the carboy will not begin to float and possibly tip and .... cause a bad day!
What I have heard other people doing is putting their carboy into a trash can/cooler like what you have, and then with a pond pump, circulating the water through an ice bath, usually in a igloo or othe cooler. The pond pump being controlled by a Johnson or other temp control... that way when you fermentation temp has cooled to the desired temp, you are not actively cooling, but if things get to warm, the pump pulls in water from the ice bucket/igloo into the fermentation cooler and drops the temp. If you go with this setup, a cooler with frozen milk jugs works great in the igloo. They last a long time and are easy to cycle back thorugh your frezzer.