You know when some ground vehicle is stepping over ground/snow it leaves trail, so I made texture containing these trails, but I don't have idea how to realize that so it looks good.

I was using particle effects (I'm working in Unity3d) and trail , but nothing gives the target result.

Any thoughts how to realize this?

One approach is to place a textured quad (with the texture) at a small z offset from the object leaving the trail set at the height of the ground/snow or object's contact height. This could be done with a vertex shader that disables depth writes.

I also think Unity has a few free asset packs that do this as well.