Firstly I am so very sorry for your loss. I myself lost my baby son so I know the devastation you are feeling right now.
However, and I say this gently, you need to allow your partner to deal with his grief in the way he wants to deal with it. Not everyone grieves the same way and forcing him to go for a walk thinking 'it will be good for him' might not be what he needs right now. It might be how YOU think you it will help but not him. Trying to make him grieve the way you want him to or telling him he is being unsupportive because he is grieving differently will just breed resentment between the two of you. If you are both going to make it out of the other side of this then you need to try and understand one another and try and see things from each others points of view. Men don't like to talk about their feelings the way we do. We want to talk it all out and cry and many men don't want to do this. My DH refused to talk about our little boy for a long time. He just closed himself off and went quiet. He did come out the other side and we were then able to pull together but initially, when all I wanted to do was talk, he wanted the opposite. Neither of you is right or wrong in how you are coping with this.
My help and support came in the form of my Mum and my closest friends along with contacting SANDS. They will give you the support that you are seeking from your partner that he is currently unable to give you.
Through their support groups I met many other bereaved mothers and their partners and I found incredible support there amongst other people who were going through the same thing as me. We bonded, we talked, we shared our experiences, we cried but ultimately we helped each other through. Eventually my DH came along to some sessions and he was able to open up to some other bereaved fathers but it took time for him to do this. It was important that I, as his wife, allowed him to find his own way there.
You will both get through this, its awful and right now it feels impossible, but one day I promise, you will find a way to smile again and rejoin the world. Your partner will get there too. But please try not to take things out on each other.
Sending huge hugs xx