Weight
This depends on if you are on a steep incline or on a flat road. On a flat road the added weight puts downward pressure on the wheel and increases traction. On a steep incline the added weight does this to some extent but it also increases the force needed to get the car moving forward. Where you put the weight is important too. If you have a front wheel drive car and throw sand bags in the trunk you will have a harder time getting up a steep hill even though you added weight. Software should be able to fix the power delivery problem, if it is a problem, but not the differential. My guess is # for # it's no worse than other large rear wheel drive luxury cars. I wonder if you could rig a braking system to brake the wheel without traction thus sending more power to the wheel with traction?I don't know about this explanation. Generally what people do to get better traction is add weight to a car such as a few hundred pounds of sand over the rear wheels. The physics is that the force is a function of the coefficient of friction times the weight, so more weight gives more force. If there really were so little friction that the car couldn't move uphill at all, it would slide downhill when stopped, a very scary situation I've been in and do not recommend. My guess is that the TC isn't set up to allow the wheels to spin together to some extent to get the car to slowly move forward. As others have said, it may well be possible for Tesla to come up with a Snow Mode for the TC and throttle control. It is all drive by wire after all.