Please define what you mean by "snake around"? If you mean you want to snake a cast iron pipe, there is no worries..

My house was built in 1964 and still has cast iron pipes for the washer drain. I'm concerned about snaking it because I don't want to cause any damage. The problem is that it drains so slow that it overflows everytime duirng the wash and rinse cycles. The original questions I have are: can I cause any damage to the pipes in the vacinity of the p-trap and how is the easiest way to get the snake down and around the p-trap?

Normally they didn't run cast iron under 2.5", instead they used galvanized iron pipe which connected to the cast iron.

What is the inside diameter of the pipe and are you sure its cast iron? Does it have leaded joints or threaded joints?

The only reason I say cast iron is because I've had three other people say it is. Now I'm wondering if it is cast iron or galvanized iron. Does this matter as far as causing any damage around the p-trap? Is one softer or more susceptible to damage than the other? 2" inside diameter. Not sure what a leaded or threaded joints is? If it's what I'm thinking, I believe it's threaded.

I can't imagine how you would do any damage to pipes like this with a snake. Also, in your query about the P-trap, I'm presuming that you have access to it so you can disconnect it and simplify the snaking? And that you've already determined the obstruction isn't simply in the P-trap, but beyond it?

Cast iron pipe is black and has a rough outer appearance..Very heavy..at the input end of each section the pipe is expanded into a hub and the next section of pipe is fit into that hub then a layer of molten lead was poured in to seal the joint.

Galvanized iron pipe will look silery or dull grey mottled finish and you will see threads on the ends of the pipe where the sections of pipe are screwed into fittings.

If the pipe is 2" it is most likely galvanized iron pipe. The problem with that is they did not have DWV(drain,waste & vent) fittings for galvanized pipe. The used pressure fitting which do not have any radius curve at the change in direction. The elbows all have sharp corners, The problem with the sharp corners is there is no way to guide a snake around the corner at an elbow.

If the run is not too long and if it is readily accessible the preferred solution would be to cut it out and replace it with PVC or ABS plastic pipe and DWV fittings.