Question

Select the subject of the sentence.

Despite the cold, several small children decided to sled down the hill behind Lidewij Vliegenthart's house.

Answer 1

The subject of the sentence is either children or hill. The subject of the sentence is the noun of the sentence.

Answer 2

The subject of a sentence is the person, place, or thing (basically the noun) that is doing something (the verb)

Because the small children were sledding, they are the subject.
Lidewij Vliegenthart may also be a noun, but it is only referring to her house, she is not actually doing anything.