A few years ago, first week of June, we took a couple of our grandsons to Jackson Lake for a week and traveled to Yellowstone one day for sightseeing. While we were there it did snow on us, but not a great deal and we only had on light coats as the weather was fine overall. By the way, it also snowed at Jackson Lake as well, getting up one morning with an inch or two on the ground. Not a big deal as it soon melted off and we went fishing and had a great time. Don't let the threat of a little bad weather deter you from taking a trip that you will remember for a lifetime.