Where I sled: Central Ontario (MOST, MSR, Parry Sound)
From my experience, proper snowmobile helmets (even the smallest sizes) are way too heavy for a toddler's underdeveloped neck muscles. They can barely hold thier heads up with one on. When my son was two and three years old, I used a good hockey helmet with a built on visor (I-Tech brand). Worked good and much lighter. Though I don't think it would be DOT approved for snowmobile use, it seem safer to me and much less expensive than a helmet that a kid would out grow in a year or two.
Have to agree with Rollo. You will have more success waiting a year, then trying to find a helmet that fits. A 2 y.o. can control their own head, but add any extra weight......The muscles are just not that developed. At that young an age, the "unexpected" can have more severe consequences. I would urge you to wait that one year before taking your child out on the trail.
And yes rollo, a helmet is "useable" only for the sport that it is advertised/certified for.
Medical Care Provider
Big East Snocross Tour
I handle the broken bodies,
My team mates handle the broken sleds
I bought (used) off a friend a bombardier full faced helmet for my kid , she was 2 and it was no problem for her to hold up . I did look at some and they were too heavy . Make sure you check the weight and get a light one . Royal distributing has some open face ones for kids too