Hello Sherry and welcome to our family, congrats on giving Winter a forever home but you realize since he is 14 years old you have some work cut out for you, it will not be so easy to win his heart and his trust but it can be done, you must be very patient with him and give him lots of time to get used to his new home.
Yes please open his door and see if he will come out on his own, you can talk to him softly and maybe play with one of his toys to entice him to join in or at least be curious about it. Some greys become protective of their cages so it might be best to allow him to come out on his own and then try to get him to step up but I sense that you are hesitant to put your hand in the position to get him to step up and if you are afraid then he can sense that and that is why he is biting you, you must not hesitate just do it. The others you have mentioned that have been successful at getting him to step up have been confident in the way they go to him and show no fear, you would be surprised at how well they can sense your apprehension.
The others have given great advice and if you follow their ideas and suggestions then you should do fine, just don't expect overnight success as you are dealing with an adult grey who has baggage and is set in his ways.
Please read thru the many threads for lots of useful information and do ask questions you may have and we will help you in any way we can.
Now all we need is some pictures of Winter, hint, hint!