That a battle was fought west of the Berezina is not in question. I supplied a quote from Mikaberidze's that states from two sources that the marshy ground west of the Berezina was not frozen hard. If you look carefully at the Esposito/Elting Atlas you will see the road to Zembino (Zembik in the Atlas) traverses marshy ground all the way from the Berezina to Gaina river.
The Atlas also shows the ground to the south, where the main fighting took place between the Berezina and Gaina, to be partly marsh, partly forest & partly open dry land.
I see no reason to change my mind that the ground was basically still a wet marsh, that is not frozen solid. The wheeled transport required a road to cross the marshes and escape to Zembino.