His focus was on Italy, Rome and Naples in particular, but he travelled as well in France, Switzerland, and Spain, writing home regularly to his steward Thomas Charlton at Stourhead and to his half-brother Henry Hugh Hoare. He visited all the classical sites and immersed himself in the landscape, all the time drawing, recording, and collecting for his house and portfolio. In Rome he discovered the work of the Swiss watercolourist Louis Ducros (1748-1810), whose revolutionary style of painting he believed would have a profound influence on the English school. He brought back large-scale Italian views by Ducros for Stourhead.
(Stourhead, one of his estates, is now in the National Trust.) His journals do relay a sense of the state of art criticism of a long ago era: An entry dated October 16, 1789:
On my return from Assisi, I visited the Convent of La Madonna degli Angeli: the church is modern, and built upon a large scale: it contains a fine painting by [Federico] Baroccio, representing the Annunciation, with the Padre Eterno, and two angels above; the colouring of the whole picture is good, though not equal in forte to that of the same artist at Perugia ; a cat, most admirably painted, is introduced in the foreground.
You can see a more detailed picture of this admirably painted cat here.
Then the French Revolution closed the continent and Hoare returned to inherited estates, devoting himself to managing the items he had accumulated abroad, and pursuing antiquarian interests in his home county of Wiltshire.
Also, and from the same ODNB article:
Colt Hoare's characteristic desire to promote British artists established him as a significant patron. He continued his grandfather's close association with the watercolourist Francis Nicholson, who recorded the now maturing landscape at Stourhead, and with Samuel Woodforde, who painted the full-length double portrait of Colt Hoare and his son for the collection of family portraits in the hall at Stourhead. Sir John Leicester of Tabley introduced him to the young Turner, who painted a series of watercolour views of Salisbury Cathedral between 1794 and 1806 for Colt Hoare. Furthermore, Turner copied one of Colt Hoare's own drawings for his oil of Lake Avernus with Aeneas and the Cumaean Sybil in 1815.
Who could doubt such a gentle existence would not continue to typify the English upper class.