Is It Possible to Operate in Winter?

An invasion that begins in january or february would have the advantage of frozen ground to support the cross country movement of large mechanized forces. In march, frozen steps thaw and the land again, becomes at best a bog and at worst a sea of mud. Winter weather is also less than optimal for reliable close air support operations. So should march? Should fighting continue into march? Mechanized forces would have to deal with the infamous rasputia or thaw.