Word class of “хорошо” in “Как хорошо”

Question

According to my Russian learning book, short adjectives are formed by taking the root of the adjective and adding:

• -ø for male (null ending)
• -a for female
• -o for neutral

Thus, the adjective красивый, -ая, -ое will give the following three short adjectives: красив, красива, красиво.

My book also mentions that short adjectives are often used after так and как.

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My question is: in the expression Как хорошо!, what is the word class of the word хорошо, and why? I’ve heard many times that it is an adverb in this case, but what I see in my learning book would lead me to say that it’s a short adjective (also because one can say Какой хороший, which is then the long form).

Answer 1

Как хорошо! is an impersonal (subjectless) sentence and the role of хорошо is indeed adverbial, it answers the question how? and not which?. But predicates in these sentences do assume neuter gender.

Other examples

На улице темно - It's dark outside
Было интересно - It was interesting
Вчера похолодало - It got colder yesterday
Проводить время одному скучно - It's boring to spend time alone
Крышу сорвало ветром - The roof got torn off with the wind
Ему стало легче - He got/felt better

Answer 2

Depending on context "хорошо" may be an adverb and a short adjective.

It's an adverb describing conditions or states:

как хорошо!

мне хорошо - I feel good

на улице стало хорошо - it (the weather) became good/nice outside.

It's a short adjective when describing objects and other things:

Вино хорошо - wine is good

Представление было хорошо - the presentation/performacne was good

Honestly speaking, "хороший" is used not very often in its short form so both examples don't sound really natural.