Drug both of our boys around in a sno coach from 0 to about 6 years old. Couple things worth noting. They dont need anything suuuper warm in the coach. Especially if the sun is out. Those things get warm. Even below zero days. Mine would routinely ride up fornt for a while then get back in the coach to warm up.
The clothing matters when they're out playing in the snow. 2 yrs old is tough for boots, not much available. We always used the baby Sorels, but they are too short and would come off their feet = ducktape them on, problem solved. If you can find a little pair of Muck or Bogs boots, insulated, they are much better. Taller and completely waterproof. Some little wool socks and they are good all day in those.
Helmets, we used ski helmets until they were about 5-6 yrs old.
Clothing, both boys now have had FXR gear for the last couple years (7 and 10 now and both riding their own mchines). As little ones, we bougth quality ski gear, typically in the spring at the blowout sales. Have had a couple Obermeyer coats and pants that went thru both boys, got 4-5 years out of those sets.
For little ones, Columbia makes a decent snow suit, but it is not even water resistant.
Not sure if you're new to the sno coach thing, but a couple things I learned, thankfully not the hard way (you'd be surprised how big a kids' eyes get when he has the chit scared out of him though ! haha). Dont ever leave the machine idling near a downhill slope! Make sure you have the safety chain hooked up!
Each incident only happened once and it was after several years of incident free riding, but worth passin on.
Seats are hard. At 2yrs old, strap the car seat in it for the kid. Safer and more comfortable. After that we used boat cushions velcro to the seat bottoms.
Oh and up to age 5, they napped longer in the snowcoach than at home! They were both good for a couple hrs of nap time a day in that thing.
Have fun!