The wires are held up by the pull from the poles. The force on the wire between two poles is the sum of
1. gravity, mg
2. the tension, T, in the wire near one pole
3. the tension, T, in the wire near the other pole.
The total force had better be zero- otherwise the wire will start to accelerate.
Gravity points straight down. To cancel it you need for some of the tension forces to go up. They point along the wire. If the wire were horizontal, none of the tension force would point up. So the wire has to sag a little, say by an angle θ from the horizontal.
2Tsin(θ)=mg, to make the vertical force come out 0. T=mg/2sin(θ)
You need for θ to be big enough to make mg/2sin(θ) small enough so the wire can supply the tension without breaking.
So that part was easy. I don't know why it's better to put wire fences in warm. Maybe a reader does.
At least where I grew up, we never strung fences in the winter because the ground was frozen and it was too hard to dig the post holes.
(published on 02/28/2011)