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Originally, in British English, the verb summerise was used intransitively in the sense: to spend the summer.

This verb is first recorded in the following title: The Sea Side, a Poem, in a Series of familiar Epistles, from Mr. Simkin Slenderwit, summerising at Ramsgate, to his dear Mother in Town.

This epistolary poem, first published in 1797, offers an upbeat account of a summer spent at Ramsgate, a resort in Kent. Simkin Slenderwit * applies to Ramsgate the kind of amiable satire that had been popularised by the English poet Christopher Anstey (1724-1805) in The New Bath Guide: Or, Memoirs of the B——R——D Family. In a Series of Poetical Epistles, first published in 1766.

* The name Simkin Slenderwit refers to Simkin Blunderhead, the son’s name in Christopher Anstey’s The New Bath Guide.

These are, in chronological order, the earliest occurrences of the verb summerise that I have found—the first five refer to the above-mentioned epistolary poem by Simkin Slenderwit:

1-: From Varieties, Literary and Philosophical, published in The Monthly Magazine, and British Register (London: Printed for R. Phillips; and Sold by J. Johnson) of June 1797 [page 460, column 2]:

Mr. Burgess, bookseller, of Ramsgate, has announced for publication, during the summer, “A Series of Familiar Poetical Epistles, from Mr. Simkin Slenderwit, summerising at Ramsgate, to his dear Mother in Town.”

2-: From The British Critic (London: Printed for F. and C. Rivington) of November 1797 [page 550]:

Art. 23. The Sea-Side, a Poem, in a Series of familiar Epistles from Mr. Simkin Slenderwit, summerising at Ramsgate, to his dear Mother in Town. Folio. 52pp. Thanet, printed for Mr. Burgess, at Ramsgate; and sold at all the Circulating Libraries. 1797.
If Slenderwit be not the real name of the writer who has thus vainly attempted to imitate Anstey, it is exactly and strongly descriptive of his merits as a writer. Before we proceed ten lines, we encounter this elegant couplet:
We got jostled, and push’d from the wall, Lord deliver ye!
And taken, no doubt, for lackeys out of livery.
Mr. Slenderwit’s poetry will, probably, occasion the same suspicion as his appearance; except that a lackey of such talents, would hardly rise to the dignity of being out of livery. We strenuously advise him to write no more Poetry. Not a spark of wit or genius appears in this attempt.

3-: From Domestic Literature of the Year 1797, published in The New Annual Register, or General Repository of History, Politics, and Literature, for the Year 1797 (London: Printed for G. G. and J. Robinson, 1798) [page 294, column 2]:

“The Sea Side, a Poem, in a Series of familiar Epistles, from Mr. Simkin Slenderwit, summerising at Ramsgate, to his dear Mother in Town.”

4-: From the following title:

The Sea-Side, a Poem, in familiar Epistles from Mr. Simkin Slenderwit, summerising at Ramsgate, to his dear Mother in Town. The Second Edition, with great Improvements, and an Appendix (London: Printed for T. N. Longman, 1798).

5-: From The Critical Review; Or, Annals of Literature; Extended and Improved (London: Printed for A. Hamilton) of July 1798 [page 348]:

The Sea-Side, a Poem, in a Series of familiar Epistles, from Mr. Simkin Slenderwit, summerising at Ramsgate, to his dear Mother in Town. Small Folio. 1797.
Of the numerous imitators of Mr. Anstey’s Bath Guide, we think Mr. Simkin Slenderwit not the least successful. He exhibits much humour and quaintness of observation, in a galloping kind of poetry suitable to the subject. His occasional inattention to the rhyme is reprehensible, as it arises more from negligence than from want of power.

6-: From The Monthly Review; Or Literary Journal, Enlarged (London: Printed by A. Straban; for R. Griffiths; and Sold by T. Becket) of November 1799 [page 350]:

Art. 43. A Journal of a Tour to Scarborough, in the Summer of 1798. 8vo. 1s. Printed at Wisbech.
In this summerising tour from Wisbech to Scarborough, we have not found our nameless describer an unpleasant companion. He is a man of observation. He is also a man of reading [&c.].