Charlie Pridham writes

Well there are several reasons a climber may choose to be evergreen,
firstly it never freezes and day length is alway long enough for growth.
such plants are usually tender.
Secondly its a plant that grows amongst deciduous plants and is hoping to
take advantage of the winter light when the leaves drop. Ivy is the
classic example. But although Ivy is sometimes hardy (Hedera helix is
actually quite variable in this respect with several clones being quite
tender) generally plants adapted to climbing tree trunks in forest are
protected from the worst of the cold and a great deal of the wind, this
makes all the Evergreen climbing hydrangeas dodgy in exposed positions.
Thirdly its not wet enough to grow in the summer months so the plant does
most of its growing and flowering in winter like the Clematis cirrhosa's
(plants like this should really be called winter green rather than
evergreen as they will quite often shed their leaves or go dormant in hot
summers.
Sadly there is no scenario where being evergreen in a cold exposed
location is an advantage (apart from to gardeners!)

Though it's a strategy which works for a lot of conifers.

And holly - though that may be to help holly take advantage of leaf loss
of the trees surrounding it, in other words, not a cold, exposed
situation.
--
Kay