Depends what you want out of your trail ride.
Our kids have been going with us since they were 6months old, either with a kid harness to ride with the adult, a snowcoach, to riding up front hangin on the mountain bar, to driving with mom or dad on the back to now running their own machines starting at about age 8.
At 4 years old you're not going to get very far IMO with a kid piloting his own sled. At age 7-8 it is tough to get more than 20-25mi in a day, all groomers good weather. Pushed the kid about 50mi one day cause we made a wrong turn and he was a tired pup after about 35mi. Ended up towing his machine out because he was too exhausted to handle anything more than pulling the throttle in a straight line.
I never even started them on 120s for this reason. Snowmobiling is MY time too and they will have to be happy with one of the other options until they are old enough (getting there now 7 and 10, 1st yr this year for the 7y/o riding solo, 3rd year for the 10year old) to somewhat keep up. And the 7y/o will make me very nervous the first few trips, but he has alot of time under his belt on the wheeler with me on the back and now is to the point where I dont have to correct him about staying to the right, how to throttle, steer and brake in different situations, slow down and move over when passing oncoming riders or vehicles etc.
I'm not spending hours of prep/unloading, hours of driving to watch my kid do laps in the snopark or go 5mph for 5mi then turn around and head out.
Also, unless it's flatlander trails with no drop offs off the trail, 4 is definately too young to trust that they will steer it correctly 100% of the time on the trail. Oncoming sleds, staying to the right, EVEN when that side of the trail drops off 100' into a gulley. These are not skills and capability kids are able to process or control at that age. Prolly dont even know left and right yet 100% of the time.
Trail riding is completely different than doing laps around the yard or meadow. Think about it this way, would you trust the kid to get on his bike and ride it unsupervised, on the street or road, crossing intersections and bridges with no guardrail? Becasue that's what it is once you turn them loose on the trails, even if you're only 150' behind them.
My kids are as involved in the sport as anyone's and I love it, but don't put your 4 year old on the trail I'm riding because I'd hate to come around a blind corner and find him hugging the wrong side of the trail and run him over. Or cause harm to myself/family due to the same situation.