Is a purchase of a seasonal cabin HMDA reportable?

Based on the short description I would say yes. Appears to be a vacation home, no different than some one purchasing a lake home or ski resort home for seasonal use.

Related question - If the customer secures the purchase of the cabin/vacation home with their existing residence, which property do you use for reporting?

I've always thought you reported the property being purchased/improved. But am hearing you use the collateralized property in this case. If not the purchased property, is it still a purchase or a refi?

For purchase or refi, you report the property taken as collateral. For home improvement, you report the property being improved.