It sounds very much like vortex interaction. I think this navigational and hunting stuff are red herrings.
I have seen contrails break up into sinusoidal patterns before - usually not very long lived. If you fly up close to a contrail you see two distinct sections. The first is a tight spiral and the second a diffuse apparently structureless haze. They often separate, with the distinct spiral dropping away below the haze. Two engines produce two spirals and if these interact you can get some very interesting shapes formed (like the pic above).
I doubt if it is to do with the cold either - more likely the airflow up high being smooth and slow.
Look carefully into the water behind an oar, or a vertical structure stood in water. At certain flow rates, vortices are shed from the tip of the blade and interact downstream in a vortex street. These often form sinusoidal patterns which then break up further downstream. Higher velocities give more random shapes and beyond that it all blends into turbulence. Very slow velocities will provide a more stable downstream flow.
Contrails are a bit like the oar above, but in three dimensions (water in the above example is 2 dimensional because of the surface). The difference in viscosity of the fluid (air) makes the velocities very different for the same effects in water.