I have not touched one of these but.... I would sure be looking at everything else first, especially the engine. Testing compression is far easier than a pump swap. Does it use oil? Have you tried to check blowby? Valve adjust? Gray smoke only on a cold start just means it is not getting all the fuel burned. That can be many things. Does it have an intake heater?
Others here are probably more up on common failures but in my experience, a bad pump just means it is worn and internally bypassing so it can't achieve the flow needed at pressure. That usually stands out more at WOT. Maybe you are fighting a fuel supply issue that is amplified with the higher viscosity fuel in cold weather?
As to the DIY rebuild, pumps are much more precise than an engine. Component tolerance can be .0001". If you don't have the tools and experience to measure such values, it might be better to farm out, and I would sure want a pump tested before reinstalling.
OH, let me share my recent duramax experience. Truck will limp if pushed too hard, otherwise runs perfect. It was determined through testing that the desired fuel pressure at the rail is commanded to 26ksi, but I can watch actual pressure roll back to 18ksi. Some might look at the pump, until I tested the fuel return rates on some injectors. All injectors will return "a little", but mine are many times higher than the service limit. So the pump 'may' be fine and just cannot keep up with the volume demand at higher engine load PLUS all the return fuel off the injectors. I will replace injectors first because they are certainly toast, then see where I am.
Another test that I did was to command the pump to full rail pressure at idle, which makes sure the pump can even do it. It had zero issue with that.