Bare, frozen ground versus wooden platform at ambient, sub-freezing temperatures? Clearly the platform is better because the ground is (1) more thermally conductive so it takes away more heat even after steady state is reached and (2) has a higher heat capacity so more BTUs / calories are lost getting it to steady state.
But you asked about frozen ground with snow cover versus a wooden platform. Snow is much more insulating than ground, until it melts. So if the snow stays above 32F, you’re insulated from the potentially colder ground. That is going to require a fairly good pad like R-4 or better in many conditions. (And even if the snow melts, that means the bottom of your pad is at exactly 32F – that’s better than sub-freezing ambient temps).
Whereas the wooden platform, usually made with gaps, would, yes, let some air up against the bottom of your pad. But that’s only in the 1/2″ gap versus 3-1/2 or 5-1/4″ width of a board – so mostly, your pad is resting on wood. The top of each board would warm a bit from the heat lost through the pad, but not much.
Heat-loss wise, I’d estimate not much difference. Whether on a frozen platform or frozen frozen ground or frozen snow, you have to have good insulation under you. But whatever heat you lose to the wooden platform would dry it out, while heat lost to the snow will melt it. Seeing as all your gear insulates better and weighs less when dry, I’d go for the wooden platform.