I've been thinking about this one. I guess it depends based on location but at least since you're talking about Utah the environment argument in the context of paid parking is way overplayed imo.
Don't get me wrong, carpooling in general only has one downside in that by getting more skiers up the hill it can make crowding issues even worse, otherwise it's only benefits, so it's certainly not a bad thing, and a very good habit for people in general to have in their lives, but it's just not making much of a difference from an environmental standpoint in the context of skiing in Utah imo, and there is the flip side of the cost of paid parking to skiers too, here is my reasoning:
Lots will be full regardless of how many people are in the car and people will be turned around anyway, just way too many skiers here and not enough lift-served terrain to supply the ever-growing demand. So having say 1000 cars in the lots has the same environmental impact regardless of how many people are in those cars. One could actually even argue less people in the car uses less gas and pollutes less too. But also, more people in cars might need less cars turned around? Although I'm not sure because I think it's more of a time-of-day based tipping point deciding whether or not people make the drive up, would need data to confirm this.
But I mean regardless, I can't help but think this is a drop in the bucket in the grand scheme of things and much more could be done. I think it's the lazy excuse resorts use to justify paid parking when the reality is that the only driver is revenue but they can't publicly admit it. There is now parking limitations (either paid or restricted) in 3 out of 4 of the cottonwood canyons resorts and traffic/parking is as bad as ever.
So I think the upside of carpooling is getting more skiers on the hill, but environment-wise in the context of skiing in UT I think it'd be a marginal impact at best and virtually no impact on traffic issues.
Deer Valley has all but announced that they will implement paid parking next year to "help with traffic and parking issues". This is of course bullshit, but I get it, from a business standpoint, resorts would be dumb not to do it, there is just such overwhelming demand that no matter how obviously greedy and unpopular the measure is, people will pay and they will always sell out.