the 1770s to 1790s were the times of America's founding and the hottest time of classical music in Vienna. Did Washington, founding fathers and early presidents enjoy music and culture from Europe at that time?
The powdered white hair look associated with Washington and the first few presidents is fashion contemporary with the glory age of classical music and Vienna in the 18th century
Disclaimer that this is not my area of expertise (at least with regard to the American reception of European music), and this may not be in depth enough for the sub's standards. But since it's been over a week and you haven't gotten any replies, I figured I could throw in one piece of knowledge I do have on the subject. I guess we'll see if and when a mod reviews this response.
But some facets of European literature (including musical literature) definitely did cross the ocean. Consider, for instance, the following letter from Thomas Jefferson to John Adams, written in 1814 (Admittedly a little after the period in question).
https://founders.archives.gov/documents/Jefferson/03-07-02-0341
That poem in the middle, there. That's an aria by the main opera poet of the eighteenth century: Pietro Metastasio. The man who penned Operas set by the likes of Handel, Pergolesi, Gluck, Haydn, and Mozart, among many others. So clearly, Jefferson is aware of Italian opera.
Moreover, Jefferson was also an avid violinist, and his extensive sheet music collection contained works by Mozart as well as countless other European masters. So, for Jefferson at least, European music was absolutely at the forefront of his life. But whether or not this extended to other founding fathers is something I cannot answer. I suspect that it did to an extent, insofar as the founding fathers do exhibit clear awareness of European literature and culture more generally (especially in the domains of political philosophy, but also literary products like Addison's Cato), but Jefferson is definitely a special case given that he was an active musician.