Back when I was on a volunteer ski patrol I carried a webbing harness, carabiner, rappel device and about 80 feet of 7 mm accessory cord. The entire set up weighed about 2 pounds and fit into a waist pack. At that resort, 80' was enough to get down from most chairs using double strands and all the chairs on a single strand. The 7mm diameter cord is strong enough and tough enough for that type of use and will work controllably with several types of rapel devices. I carried additional slings to be able to lower other people as well. If word came over the radio, or by a patroller under the lift, that a chair was going to be inoperative for and extend time, we patrollers could self evacuate and then assist others with gear from the ground.

As far as climbing on the cable goes, good luck. The weight and bulk of heavy clothing and the awkwardness of ski/snowboard boots would make this very challenging to say the least. Another consideration is what would happen if the chair started moving? Would you survive an encounter with the wheels of a lift tower cable support? If you are rappelling when the lift starts moving it is not as nearly as bad.

I still carry a similar rapel setup in my inbounds ski pack nowdays, just in case.