Posted: 07/12/2014 at 16:19
Hi Triple J, welcome to the forum.
unfortunately Mike has a habit of writing rambling posts of irrelevant information, freezing water in pipes???! Anyone that has pruned a conifer, would tell you it's resin that bleeds out and this only freezes below -50 Celsius, hence conifers living in some of the coldest environments on the planet.
Your neighbour has leylandii that has got out of control, you are allowed to trim off branches that are over your side as long as you give them back to your neighbour. Cutting back beyond the green growth, into the brown wood of leylandii will cut that branch, so unless you plan to remove all the green growth, it will survive.