Learn Swedish: Åh, vad fint!

Yes, vad usually means "what" in questions. But in exclamations like this, it translates to "how"! You will see this pattern a lot: vad followed by an adjective means "how [adjective]". For example, Vad roligt! means "How fun!".

Why does fint have a -t at the end instead of just being fin?

When you make a general exclamation without referring to a specific noun, Swedish defaults to the neuter form of the adjective. This form usually ends in -t. Because you are describing a general situation rather than a specific en word, we say vad fint! instead of vad fin!

Could I say Åh, hur fint! instead, since hur means "how"?

No, that would sound unnatural. While hur means "how" in questions (like Hur mår du? for "How are you?"), Swedish always uses vad for exclamations that mean "how [adjective]!".