I see you are writing from the UK ... glad to see so many folks interested in R/E in the states now!
I believe you are asking do you have to pay property taxes for a holiday home? The answer is, YES. One is not exempt from paying property taxes (I suppose some exceptions can be argued like certain inner-city zones, etc., but surely not many). It is a fantastic time to buy here, and hopefully we can call you neighbor soon.
Thanks for writing!