As long as you’re moving and not out for hours at a time, the boots you have should be ok. There’s a huge difference in clothing needed to keep warm when moving and when standing still.
Long underwear under jeans should be ok. The long underwear will keep the heat close to your leg so the outside of the denim stays colder and snow is less likely to melt on it. Brush off before you come inside to avoid getting damp. If you do think you’ll be rolling around in the snow with the kids, a cheap set of rain pants over the jeans will shed the snow.