The thing about a walking horse is, they like to go. Normally. They are good solid horses with giant hearts. They are kind and loving and really faithful friends. Because of there ground eating glide ride type movement, they very popular trail horses. It sounds to me like yours came from folks that liked to get on and go.
My first walking horse was like that. The moment you got on him, he took off like a bolt of lightening. I had to tie him to a fence to mount and then unhook him after mounting in the beginning (That's a very stupid thing to do, don't try it). He took so much arm strength to keep slow and to stop in the beginning until I learned how to use my seat with him.
Because of their side to side motion, you use your seat just a bit differently then a regular horse, even your leg position is a might different.
You have a couple options, one is to get an instructor, and it doesn't have to be one that specializes in walkers, especially if you are a trail rider, but it needs to be one that has real experience with walking horses. Have them check your bit. Make sure you are using one that works for that horse. I'm not saying rush out and buy a stronger bit, just make sure you have one that works for that horse. If it's used to a port with a long shank, then a snaffle may not be such a good idea (not that, that IS your problem - just a consideration).
My first walker did get to where you could ride him with zero rein contact at a slow walk, but it took practice. My new walking horse is SO lazy. She mosies along and never wants to go first.
Things to consider are that this horse is just too much for you and you need to trade him for something slower, you need an experienced rider or trainer to work with it for you, or with lessons you can continue. Don't make a quick decision based on the rantings of folks that read your first post.
TWH's are wonderful horses, especially for first time owners. Asking for help is a wonderful thing and an online forum is great for ideas and advice, but it sounds like you do need a real person to evaluate where you are at.
I wish you the best of luck.