Snow usually leaves two options; take photos while it is snowing or wait for the sun to come back and get them then. It’s a preference thing. The sun will give you some golden glow, but cloudy snowy days will give you a more even lighting and, well, snow in the air. Of course, you can always do both and you should, but I like the lighting better with clouds and snow in the air. Also, I find the shady areas tend to look blue on sunny days when snow is involved.
For kids, just let them play. They should provide all the action you need for decent photos. Occasionally, you can throw out a “look this way” but otherwise let them do their thing. Believe it or not, kids will figure out how to play in the snow. And if they are having fun, you should be able to pull out some amazing photos from their activities. All that stated, one piece of advice I’d recommend is that you wipe their faces off before they go outside. Don’t worry about hair prep too much unless it is distractingly unruly, but kids are wild, so let their hair be a little wild too.
Once again, these had a high shutter speed to freeze the snowflakes in the air. I went with a higher ISO and a lower f-stop number to compensate for that. I’d recommend practicing with a lower f-stop number if you are going to try that because it can be tricky. Fortunately, it is a digital age so practice can be plentiful.