Ultimately this is a question that only you can answer, but I'll share our experiences skiing with 35 month old.
This wasn't at Jackson Hole (or even in the US) but I think it is transferrable (we have skied in North America and apply the same principles there).
Our son has always travelled with us to ski and we have found that this has paid large dividends as he got older (we took him to North America for the first time when he was six and he thrived). We made a conscious decision that ultimately we wanted to ski as a family so better to get used to it early rather than later - on the assumption that he would think that it was normal family behaviour. What do you and your wife want medium to long-term? Is this trip a one-off or are you likely to travel to ski regularly? (By the way these questions are for you to consider - don't feel obliged to answer them publicly).
We found that larger ski resorts often had better child care facilities (larger, lighter, qualified staff, good staff to child ratio's, better resourced etc which all led to more settled child and less guilty feeling parents). We were specific about using one that was our equivalent of state licensed. JH is a state licensed facility so that would be a plus for us. I would be tempted to contact the centre and see if they could send you some images of the facilities and tell you what the staff to child ratio is.
Our son was used to childcare at home so going to daycare at skiing was't too bigger leap. By 35 months he was articulate enough for us to have a conversation with about it so he was excited to go.
If your son goes to child care at home does he hang out with the four year olds or the two year olds if the group is mixed? Our son gravitated to older kids at that age and had the language to keep up with them and he wasn't particularly keen on toddlers, so at 35 months we negotiated with the resort we went to and enrolled in the 3-5 year old kids centre which made a huge difference and we had no problems with him keeping up in the skiing bit. I think we would have had a different outcome if he was in with the 0-3 year olds (because he was at the age where "I am not a baby"). How well do you think that your son will settle at child care? What age group will he settle best with? Is it a deal breaker if you cant get the best fit?
Does your son still sleep during the day? If yes, is he likely to sleep at child care - ours didn't (settle easily at childcare for sleep ever) so until the year he was 35 months afternoons at ski resort childcare could be a lottery.
Food - What is the ski school typical menu? How does this fit with your sons eating habits? Hungry kids hate skiing. We did send some snacks that we knew our son would eat, but he was pretty easy going food wise.
Accommodation - we get accommodation / lodging that has at least one bedroom so that we could chill out with a glass of wine after little kids were in bed (our son was a bit of a party animal and would not ever sleep in a room if there was any hint of something more interesting). So the question is can you come up with a lodging solution that means that you will all have a good holiday and is within your preferred budget?
The good thing was that we discovered that the holiday was fun. If you normally have fun with your son on holiday then chances are you'll all have fun skiing at JH together.