Greatly depends on the weather forecast. In cold months, around here at least, subsoils directly beneath the topsoil are 2% to 6% above optimum moisture conditions. If one hopes to dry subsoils to allow for fill placement, best to strip topsoil as soon as a dry 'window' is forecast. A trick many graders do around here is to strip topsoil at the end of the day if nightly forecast calls for low humidity conditions. Even if below freezing at night, 'jack-frost' tends to form on the wet subsoils (water rises to the surface of the subsoil and freezes when it hits the cold air - kind of pretty when it gets 2" to 3" in length). The first thing a good grader does in the AM is lightly scrape the surface to remove the very wet material (can do when ground is still frozen), scarify the underlying material, and begin fill operations.
The most important thing to remember is the soil type - who cares when soil is sandy. When clayey or silty material at near-surface, it really matters
Normally you will commence filling immediately after you've thoroughly stripped the area of all vegetation and topsoil. The reason for this is two-fold. You'll want to protect the underlying soil from a deep freeze (a little frost won't hurt under a deep fill) and since you already have earthmoving equipment on site with personel mobilized, it makes sense from a production standpoint to start cuts and fills right away. Here in the West the addition of moisture under the initial lift of fill material is usually neccessary to act as a binder between the existing grade and any new fill material. Remember to add water UNDER each new lift of material since moisture will "pump" up under the weight and dynamics of compaction equipment but it is extremely difficult to force moisture downward into the fill. At the end of each shift add an additional dry lift across the entire fill area to act as insulation against overnight freezing. Do not compact or blade off this top insulation layer-but water and roll it in the morning.
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