I am not a car expert, so I will try to make this question as brief as possible while including everything I think might be relevant. My car is a '96 Infiniti i30t, automatic transmission.
Last night I got stuck in snow. With my cousin’s help, I was able to get the car free. Basically, what I did was inch toward the more packed in snow on the street by placing my floor mats in front of the front wheels (my car is front wheel drive) and pushing from the rear in a sort of rocking motion while my cousin attempted to accelerate in 1st or 2nd gear mode. We made progress, but he had a habit of letting the wheels spin at high speed doing nothing for what I am afraid is too long. If it kept going for 7 seconds or thereabouts I told him to stop, but it happened a few times. At one point I smelled hot rubber and made us wait for a minute to avoid warping the tires. Eventually he left to get more tools and I continued to inch forward using the floor mats. I eventually got the car all the way out this way, but since I was by myself toward the end I had to reverse and back up a few times before going forward again in 1st or 2nd to get momentum.
My question is whether I should be worried about tire or more importantly transmission damage from this. Does anyone have any insight?
EDIT: This morning I drove the car around the neighborhood for about 5 or 10 minutes, and did not notice anything different as it changed gears. It drove as well as it had before. Not sure if that is relevant.