Thus here,

'Eseguiti da Gaspare Bargioni e Niccolò Contestabili, [i trompe l'œil] rappresentano la moda dei primi decenni
dell’Ottocento nel far decorare stanze “a boscherecce”, finte
architetture, rovine e prospettive che aprono gli ambienti su
spazi campestri.

The frescoes, by Gaspare Bargioni and Niccolò Contestabili, were the last word in fashion in the first few decades of the 19th c., when rooms were decorated in “boschereccia” or “woodland” style with illusory architecture, ruins, follies and false perspective leading the eye out of the room into make-believe orchards and fields.'
(www.palazzostrozzi.org/allegati/allegati/06_passaporto_inga... page 81)

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Note added at 8 hrs (2012-07-05 07:08:57 GMT)
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Here are the Italian and English excerpts from a site describing Palazzo Sanguinetti in Bologna:
'Al piano nobile, "...se si segue il percorso museale - scrive nella guida del museo Paola Foschi - la stanza alla boschereccia (sala 1), che era utilizzata come sala da pranzo ed era detta Sala del Convito, è prodotto della fantasia di Vincenzo Martinelli (1737-1807), che immagina paesaggi ricchi di verzura e di architetture classiche in lontananza; queste si fanno vicine a circondare l'astante nel gradino illusorio che sorregge erme e statue di Bacco e Cerere, opera del giovane Pelagio Palagi (1777-1860).'
(http://www.museomusicabologna.it/palazzosanguinetti.htm)

'On the first floor, "...if you follow the designated course through the museum" - Paola Foschi writes in the museum guide - the Woodland Room (Room 1), which was used as a dining room and called the Banquet Room, is a product of Vincenzo Martinelli's (1737-1807) imagination: he illustrates landscapes rich with greenery and classical architecture in the distance. These classical elements surround the onlooker in the illusive step that supports hermas and statues of Bacchus and Ceres, works by the young Pelagio Palagi (1777-1860).'
(http://www.museomusicabologna.it/palazzosanguinetti_eng.htm)

Here is how 'boschereccio' is used in another context, but still translated as 'woodland'
The Giardino Boschereccio (the woodland garden)
It is located opposite the Casino Nobile and it was designed by Flaminio Ponzio in 1606. Initially the project included 23 squared sectors containing different types of trees, limited by tall and shaped hedges adorned with precious sculptures, such as the Fontane Oscure (Darks Fountains) and the Grotta dei Vini (Cave of Wines). Today this division has almost completely disappeared and the vegetation has been supplemented with new species, including evergreens.'
(http://arrangeyourvacation.com/travel-blog/romes-villa-borgh...


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Note added at 9 hrs (2012-07-05 08:02:20 GMT)
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Hi Lorraine!
Where does the 'Native American rustic style they claim to have invented' come from? Who's 'they'?
There is no doubt about this term being Italian and derived (yes, you guessed it) from 'bosco' [re. boscheréccio (ant. boscaréccio) agg. [der. di bosco] (pl. f. -ce). – Di bosco, che cresce o vive nei boschi - Treccani online].
Am I missing something here?

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Note added at 9 hrs (2012-07-05 08:34:31 GMT)
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I see what you mean, now.
That's why I think you should keep the Italian combined with the English. That would avoid any misunderstandings.
Ciao!

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Note added at 2 days18 hrs (2012-07-07 17:29:28 GMT) Post-grading
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Thank you, Lorraine!