Some interesting ideas here. Lets look at the options.

If you've got 3 people stranded on a chairlift, you only need to get one person lowered down safely (right)? It only takes one person to go for help. It might be possible to use belts, and skis to lower one person down by 20-30 feet. Then maybe they could drop the remaining 20 feet, land safely in the snow, and walk out for help. It all depends on what the terrain is like underneath the chair lift. I doubt that you could lower a person the whole 50 feet - not enough gear. The main problem with this procedure is that once you start lowering the person, it's going to be nearly impossible for them to climb back up. So you have to get it right the first time.

I like the idea of climbing off the top of the lift, going along the cables, and going down one of the support towers. Or maybe I should say - it's intriguing. But it's also quite dangerous. If the weather is bad, and esp. if conditions are very cold and icy, the chance of taking a bad fall could be quite high. If you were going to attempt something like this, it would be smart to attach some kind of belt around your waist, so you could connect the belt to the cables as you do the horizontal section of the traverse. That way the belt can support some of your weight. But I have to tell you that this whole procedure could be enormously strenuous, esp. if the person climbing cannot find a rest position a few times during the escape.

Back to your original question. Yes, you can bundle up low-diameter paracord and keep it on you. But rapelling on this stuff is much harder than you think. Even if you have a single strand 9mm rope (the standard lightweight rope for technical climbing), you will find that there is marginal braking ability with normal rappel devices. It can be done, but you need to be careful selecting the right rappel device before you do it.

Small diameter paracord would be a major problem. It MIGHT be possible for one person to tie into one end of the cord, and then wrap it around the metal on the chairlift many times to add friction, and then have the other 2 people lower the person down. That might work. But before you rely on paracord, i suggest that you actually try it out (SAFELY!) at home. You'll see what I'm saying.

other Pete