The term 'foliage trip' appears in a Vermont newspaper in 1909. As reproduced in the Chronicling America corpus of US newspapers, it is there modified by 'autumn':
They were celebrating their seventh wedding anniversary in taking an autumn foliage trip through the Berkshires, the Green mountains and the Connecticut valley....
(The Bennington Evening Banner, October 15, 1909. Emphasis mine.)
The term reappears without a modifying 'fall' or 'autumn' in 1931, in The True Republican, Sycamore, Illinois. Here the context and the date of the publication make 'fall' or 'autumn' superfluous:
In 1964, an appearance in Lancaster Farming (Pennsylvania) is modified by 'autumn'. Subsequent appearances in 1971 and 1973 are found in newspapers from Missouri and Illinois, where the term is modified by 'fall'. In 1975 and 1981, the term appears in Texas newspapers, unmodified. In 1983, 1985 and 1995, the term appears in three more Texas newspapers, modified by 'fall'.
All the above appearances can be viewed in context by following links from the two pages of an Elephind search for 'foliage trip'.
Beyond uses (including more recent ones than are shown in the Elephind search) in the Northeast, Mid-Atlantic, Southeast and Midwest states of the US, a search of the NOW Corpus reveals an appearance in Toronto.
The more common variant, 'foliage tour', likewise occurs in newspapers (digital and otherwise) published in the eastern and midwestern regions of the US, as well as southeastern Canada (as evidenced by appearances in Toronto Star). This variant first appears in the Elephind corpus in 1916, in the "Travel" section of the Richmond Times-Dispatch (Virginia), where it is used in the title of an pseudo-news advertisement describing two tours: "Summer Vacation Tour and Autumn Foliage Tour of JAPAN". Four later appearances in 1917, in newspapers from Pennsylvania and New York, are also modified by 'fall'.
After 1917, the 'foliage tour' variant does not crop up again in the Elephind corpus until 1956, in the Lancaster Farming newspaper from Pennsylvania where 'foliage trip' turns up in 1964. Subsequently, approximately 200 (discounting duplicates) instances of 'foliage tour' appear in the Elephind corpus.
About your questions:
Where do people use “foliage trip”?
As detailed above, to the best of my external-evidence-based knowledge. Having grown up in the midwestern US, I can attest from personal experience that the terms 'foliage trip' and 'foliage tour' were common there from the 1960s through the 1990s at least. I have no doubt they still are, but can't attest to it from personal experience.
Outside of the US North-East (in similar climates, and in climates where the beautiful colors of fall leaves isn't a thing), do people understand the expression?
Yes. There's nothing mysterious about the expression, and many English-speaking people will be acquainted with the beauty of autumn foliage colors, if not from direct experience then from photographs and films.
Does British English have an equivalent expression...?
Not to my knowledge, although, for the reasons mentioned with respect to general understanding of the term in English, British people probably wouldn't find either expression mystifying, particularly as modified by 'fall' or 'autumn'. They might be inclined to sneer at the expression on the grounds that it's an American expression, but that's par for the course.