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I read this short story in a Sci-Fi collection when I was in middle school in the early 1980's. My school had a lot of older collections from the 60's and 70's.
The setting is a post-war Earth where, due to decades of programming and reprogramming, war robots have exterminated all of mankind. After an indeterminably long time the robots are slowly falling into disrepair and "dying". The point-of-view is one of the few remaining robots, who exists in a crumbling city where a handful of other robots also abide.
This particular robot waxes existential and likes to visit a park where there is a statue of a child. It sits by the statue and ruminates on the wars and the passing of time, etc. There is another robot who is attempting to build a new robots from salvaged bits of damaged and inactive robots but his attempts are frustrated due to the fact the robots' appendages are designed to kill humans not make things. The story ends with the main character sitting in the park by the statue and slowly being covered in snow.