I was a former geology major in college and attempt to visit as many geologically interesting sites that I can. Yellowstone is up there on my visit list.
On my last Yellowston trip, I took a portable temperature gage. You would be amazed at the temperature of the ground just off of the elevated walkways around the park. The highest temperature I read was 162 degrees about 5' from a Norris geyser basin walkway. Also there are thousands of vents spewing out toxic gases near walkways. Coupling high ground temperatures, hot water temperatures with high toxic gas levels, Yellowstone can be a very dangerous place for humans and even more so for dogs who venture off path.
We were in Yellowstone in early June and it was cold and snowed 3 of the 7 days while we were there. The other days were sunny and beautiful. Despite the 3 cold days, we were amazed how warm it was while walking in the geothermal areas. I remember taking the temperature of a walkway while it was snowing. I recall the walkway being over 100 degrees despite the air temp in the 20's and it snowing. So if you love your dogs, Yellowstone is no place to be even with a highly obedient dog.