What "How about" subject predicate object is？

Question

As we all know, the sentence "How about walking in the park?" is perfectly viable.

But where is the subject of this sentence?

And how can we define its subject, predicate, and object?

Answer 1

We use How about to make a suggestion or to ask for information. [More examples here.] It is often used in informal (definition 2) English: when speaking or writing to our friends and family, for example.

In this conversation between two friends, how about is used to make a suggestion:

Person A: How about a pizza?
Person B: Not hungry.
Person A: A game of tennis?
Person B: Too hot. How about walking in the park?
Person A: OK. And then pizza.

Here it is used to ask for information:

Person A: You don't like swimming?
Person B: No.
Person A: Or jogging?
Person B: No.
Person A: How about walking in the park?
Person B: No. I prefer lying in bed drinking beer.

Answer 2

This is not a complete sentence in the traditional sense. In other words, it does not contain both a complete subject and a complete predicate.

It is possible to construe this "sentence" as a prepositional phrase:

how about: phrasal preposition
walking: gerund functioning as the object of the preposition
in the park: prepositional phrase modifying "walking"

Of course, others may parse it differently.