Is there still snow in the end of May, beginning of June? Is it too cold for little kids to camp during this time?

The snow is long gone. It's only a little over 5000 ft, so not much different than Utah or Salt Lake valleys. We were there a few weeks ago for mother's Day and there were plenty of kids camping, including ours.

I just took my kids up to the campground last weekend. It rained a little but no snow. We still had a great time and even did the Fifth Water Hot springs hike.