moving aircraft do not have spinning drive wheels, and they start having increasing lift from the wings right away with increasing speed. I think sinking into desert sand, maybe, but not dirt on a field. A bigger concern would be excessive bumps/ditches and/or soggy bogs.

The wings on an airliner aren't producing much lift below 100mph or so. You're on the wrong end of v^2

edit: sorry, I just realised you were talking of a one off, for this plane. Naturally it'd be fine frozen, but you'd have to wait a bit, until the ground froze a bit. eg, not just the surface. Here that usually takes a month or more, because the ground takes quite some time to cool.

--

The road gets warm in the winter, even at -40C, if there is a lot of traffic. Snow is smushed, it is warmed by the tires, due to friction, and even sublimation happens.

If there is enough traffic, frozen ground can become thawed. Especally at a mere -10C. The dirt road in front of my house confirms this in winter, with potholes and wet spots, and not from salt.

Landing events have even more friction. And many aircraft are far heavier than cars.

Rare teaffic would be fine I guess, but a mildly busy airfield might be different.