We are talking about violins. Get it right. The short answer is indeed, sizing plays a role in how comfortably your violin will fit you. In my video, I address the four most common sizes (1/4, 1/2, 3/4, 4/4) that are used for ages 5+, and you can check that out here for a demonstration and more info!
The chart below goes a bit more into depth in terms of age, measurements, and some of the very smallest sizes of violins you can find if you are looking for a tiny tot!
As I mention in the video, the best and simplest way to know for sure which size will be appropriate for your child is to simply have them hold the instrument up in "playing position" on the shoulder, and extend their left arm beyond the scroll. If the scroll meets their wrist, the violin is the correct size. If the scroll reaches their palm or beyond, the instrument is likely a little too big, and it'd be best to size down.
Always keep in mind that if you are looking for an instrument for a child that is very young, they will outgrow their current instrument in a short amount of time. So, be prepared for when that time comes, and that way they can continue to play comfortably and keep good playing habits and technique!