Sorry to pour cold water on the so called solutions to the freezing cursor problem but, in my experience, there is an inherent fault with the Surface Pro that MS has refused to acknowledge ever since the product was introduced. All the fixes that have been helpfully suggested on this forum ( surface pen, battery charger, battery only mode, power only mode etc ) may work for some but not for everybody.
I took delivery of mine in September, 2018 and it was only after I received a second replacement in the summer of last year ( the replacement came with a 256GB hard drive instead of the original 128GB !!) that the problem finally disappeared. However, there was still no explanation as to what caused the fault so it was simply pot luck when it was finally solved. Pretty poor performance from a company with the size and resource of MS.
Bottom line is that my SP is now working as it should have done from Day 1 ( and is a terrific machine ) but my next laptop will not be from Microsoft. I have told MS this ( no response ) and suggest everybody else does the same. Maybe, just maybe, somebody there will listen, take action and, above all. communicate with us !