Could you prepare oxalic acid by adding HCl to a solution of oxalate, cooling it and filtering the result?

The water solubilities of oxalic acid and sodium oxalate at room temperature are 10g/100mL and 3.7g/100mL, respectively. Could you prepare oxalic acid by adding HCl to a solution of oxalate, cooling it to room temperature, and filtering the resulting mixture? Explain why or why not.