I just drove my Prius through 8-10 inches of heavy wet snow. The car did amazingly well. At times my traction control light was on when trying to get up an incline until the car got going. Then when I got home I stopped in my driveway for the garage door to open and started into the garage. The car was stuck, but then the light came on and the car climbed the driveway in about 10-15 seconds and made it in the garage. I then noticed a smell like burning tires. Maybe it was the tires from spinning. I hope that I didn't hurt my transmission or another component. Does the Prius protect iteself if it is stuck and the traction control light is on from overheating something? I think I recall that the 2nd generation Prius would not allow for wheel spin to protect the traction battery. By the way, I did notice that using eco-mode really helps eliminate wheel spin.
I am guessing the inverter was warm/hot. After a road trip this summer, with some mountain climbs and with grill blocking in, I smelled something burning/hot too.
Most likely the tires you smell. Even spinning on snow will generate a smell (but no smoke ). I haven't hurt the car spinning the tires (as much as it lets me) in four winters of driving. And I can tell you we certainly have lots of snow/ice to drive on! Do note that for the first year or two when you get the lower cases of the engine/HSD warm you will smell the wax they spray on for shipping. It may be more noticeable when in cold air.
If the smell was not from the tire spinning/burining, it could have been from the CVT system, like belt slipping between the coverter sheaves. Shown below is a typical CVT system but not from Prius obviously.
The Prius does not have a belt or pulleys. The transmission of the Prius is not a mechanical CVT. The mechanical portion has fixed gearing; not shiftable, no clutch, no pulleys, no shift bands. Only the electrical power path is variable. Tom
The TCS uses differential braking to control wheel slip. If one wheel slips and the other isn't, the open diff will prevent torque from going to the wheel that's not slipping, which is bad, since that one has traction. The TCS will brake the spinning wheel, so the wheel with traction can get torque and pull the car forward. With all the struggling you did, it was probably doing braking like this and heated up the rotors, and burnt off some dirt.