Dannie Abse A Winter Visit

We get the impression from the poem that the persona is walking through the park with his elderly mother who is coming close to death. The personas mother recognises that she is close to death - 'this winter I'm half dead son' and the persona himself knows it too. 

In the fourth stanza we can infer that even though the persona is sad about his old mothers age, he cannot express any emotion. 

From the last stanza we see that the persona doesn't want to talk about death with his mother, even though they are both thinking about it. This shows that he is sensitive and caring towards his mother as he loves her and doesn't want to think or talk about her dying. 

You could link this poem to Larkin's Home is so Sad and Reference Back - with the persona realising how old his mother is.