Snowcoaches are warm inside. You'll want to spend time walking around the thermal areas and Old Faithful and for that you can either bring clothing or you can rent snowmobile clothing at many places in West Yellowstone.
It is all about layering wearing clothing in layers that you can easily remove in the snowcoach. Here are some tips:
You clothing should handle cold down to -35 to -40 degrees F. Be sure your clothing includes a windproof, hooded outer layer with wool or other insulated garments underneath. If skiing or taking a snowcoach tour, pack a pair of lightweight wind or rain-pants for provide extra warmth on windy days. Avoid cotton jeans and sweatshirts which do not allow sweat to evaporate.
The majority of heat is lost through the extremities so go the extra length for your hands, feet, and head. Wear a face mask-style stocking cap or parka hood when you need maximum protection.
Thick wool socks and gaiters over boots help to keep your feet warm and dry. Wear gloves or wool mittens with shells that breathe to allow moisture to escape from sweaty hands.
If you hands and feet get cold easily, here is a trick that my husband uses when guiding snowmobile trips into Yellowstone. Before leaving, he takes small disposable heat packs and puts one in each glove and one in each boot, and one on the top of his head on very cold days or for anyone with less-than-thick hair. You need some type of clothing in between the heat pack and your skin, so he puts them in-between socks and boots, inner gloves and outer gloves, and headsock and helmet. Those packs will do more than anything else to keep you warm for the entire day.
Yellowstone’s high altitude and dry climate require a little extra packing. Always pack extra water and continue sipping it during the day. I know that sounds funny when surrounded by millions of gallons of frozen water, but the dry climate drains moisture quickly from people without realizing it and you get cold quicker. The added water helps.
Remember, high altitude sunlight reflected from snow is much more intense than at lower elevations; snow-blindness may occur if sunglasses are not worn. Wear dark glasses on sunny days. We even wear them on gray days. Apply sunscreen lotion to exposed skin to avoid sunburn.