I don't know if you can assume that. The fact that he spent the night in relative comfort in a tent can't be used as evidence that he wasn't capable of building a snow cave or a snow trench. (Although he himself said that if it hadn't been for the survival gear in his plane, he'd have been lost, that may not have turned out to be the case; we'll never know.)

As far as the plane "sinking", the picture in the second article shows him standing by a wheeled plane, not a float plane, and the fact that the lake was frozen over makes it unlikely he was flying a float plane. There's a considerable body of evidence that making a controlled crash landing in the trees is as safe as ditching (which I believe I read on this site somewhere). And even if he'd ditched on the lake, it may be unlikely that the plane would have gone through the ice.