OP - welcome! :hello:
Like El Burro... I have taken my current 4Runner to the snow (various resorts in Tahoe and Bear Valley) every winter since buying it in 2014 and its been GREAT! Attached pictures (b/c :worthless) are from a Bear Valley trip last winter... sorry its crappy iPhone pictures... but you can see it was snowing pretty good that morning and the 4Runner did amazing.
With 4x4 and snow rated tires, you should be fine for any conditions that you'd want to be out in (i.e., if it's snowing so hard you "need" cables/chains on a 4x4... you dont want to be out driving around in it).
I am not familiar with your tire... but the spec sheet for it should tell you if it is rated for snow... it'll have an M+S or M/S or MS or snowflake or similar rating for "snow".
As for advice... The best piece of driving advice I ever received regarding snow/icy conditions was "remember it is 4 wheel drive... not 4 wheel stop!" That nugget has served me well over the last 20 years or so as I havent ended up in a ditch yet (knock on wood

)
Also, if you get the chance... I'd suggest trying to find an empty unplowed parking lot to practice driving in... get to know how your Runner handles in 2 and in 4 wheel drive (and differences in handling) ... how it turns, slides, stops, etc. in those conditions. I did that with my first 4x4 back in college in the Squaw Valley parking lot and it really helped me get comfortable driving in the snow.
And lastly ... though it should go without saying... I will anyway cause ya never know... be prepared when you go to the snow - especially with little kids. Make sure you have proper clothing, proper equipment, emergency tools, emergency supplies, etc. Being prepared significantly increases the likelihood of positive outcomes in the unlikely event of bad things happening. Sorry to be preach-y ... I just hate seeing un prepared people from the valley driving up to Tahoe for the day and getting into bad situations and then making them worse by not being even the slightest bit prepared to help themselves.