I would like to know the species and, if possible, the exact cultivar, of this smallish tree:
(Hints: the pictures are taken today, northern hemisphere, temperate climate, and a woman living nearby says birds eat all the berries during winter)
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It looks like a very mature Pyracantha, but you can check by looking for its sharp thorns - these arise off the wood on the smaller branches, and I can't actually see any in any of the pictures. There are several varieties with orange berries: Orange Glow, Saphyr Orange, and a host of others, as well as red berried and a couple of yellow berried varieties. They produce white flowers in spring, usually around May, and this plant is often used for hedging; common name is Firethorn. Image of P. 'Orange Glow' here https://www.best4hedging.co.uk/pyracantha-orange-glow-hedge-plants-pp36.
As a point of interest, there's one called Pyracantha Mohave - it has redder berries than these, but the birds don't like the berries on that particular cultivar, although they're fond of all the other pyracantha varieties.