I know how you feel! It is the worst thing in the world to have a pet lost out there somewhere.
I haven't used a pet detective myself, but I've heard of people having good results from them. Call around and ask exactly what they do. The good ones will put out trail cameras and bait to get pictures of any animals in the area. Some have sniffer dogs specially trained to locate cats. Keep some of his bedding in a sealed plastic bag so that the scent is still strong.
Don't worry about the cold. As long as he can get out of the wind and the rain he'll be able to keep himself warm. One of my cats went missing for a month in February, when we had blizzards and minus 20 C nights. She managed to find shelter and even made her way to the house of a lady who feeds feral cats so we were eventually able to bring her home.
There is a feral cat in this area that comes round nearly every day, but refuses to come in. He's survived at least 3 winters outside. Cats are very resourceful.