My conclusion from my admittedly rather limited reading is that the thaw was in place during building and during the crossing. I quote again from Mikaberidze (page 132) describing the movement of Polish lancers west of the Berezina.
"... was sent towards Zembino. A Cossack outpost, deployed there, failed to destroy the local bridges and wooden causeways running through the marshes and across the Gaina rivulet, although these were already prepared for destruction. As Chambray explained, 'Nothing was more important than to occupy the road to Zembino because one and a half lieue [~6km] from Studyanka it crosses marshy woodland, impracticable for vehicles except when frozen hard or in very hot weather'. Wilson confirms: 'Had the Russians burnt or destroyed these bridges, the route would have been irreparably closed against the enemy's progress.'
Here we have Mikaberidze quoting two sources that indicate that the ground was not frozen hard.
Elting in The Atlas supports your view "During the night of 23-24 November, winter began to reassert itself; by the 25th, the marshes west of the Berezina were frozen enough to enable infantry to deploy off the roads". But this doesn't necessarily mean that wheeled transport or cavalry were able to move off-road at this time.