What is this hedge??

[calistaraines]

And when would be the best time to cut it back??

Looks like beech.

Agree it's beech. The leaves turn brown and crispy but stay on over winter so it's a lovely all year round hedge. The brown leaves don't fall until pushed out by new fresh green growth in the spring. It doesn't need much pruning, just to maintain the shape of the hedge - to do that and keep new growth in check you might trim in late spring and again in late summer / autumn bearing in mind if you want screening through the winter don't prune back too much in the autumn as new growth won't appear to fill gaps till spring.