Thanks for reaching out and good on you for thinking ahead to this winter! My kids are 7 and 5 and we lived in Fairbanks, Alaska for the last 6 years so I know how important it is to be able to get outside no matter the weather or temperature. Most of the advice I can give can be broken in to two categories: How to stay warm outside in the winter and What to do when you're outside in the winter.
How to keep your kiddos warm.
Layers, layers, and layers! My daughter's school sent students outside for recess in any temperature above -20°F. So my advice is based on working down to that range, and if it's any colder than that does anyone really want to be outside?
For feet, body, head and hands we would start with a base layer. For their feet, it would be a nice thick wool sock. For their bodies it was a midweight wool baselayer, and for their hands a liner glove. Fleece balaclavas for their heads. The trick is to keep these layers loose enough that they aren't restricting any blood flow to their extremities but also snug enough that they fit comfortably under other layers.
Over those base layers go mid layers: a heavier weight fleece pant and shirt.
Over those go their outer layers: Warm winter boots on their feet that are big enough to accommodate their socks and not be restrictive. Insulated bib-style snow pants and an insulated, hooded winter jacket (if it is REALLY cold then we may add a thinner down jacket under the heavy winter jacket). A warm hat that fits over their balaclava (again, if it is REALLY cold, we have adult size fleece neck gaiters that we put on them as well). On their hands they wear mittens that fit over their liner gloves and cinch down snug to prevent snow and cold air from getting in there.
Typically that does the trick for heading outside and being warm for a good hour or so of play time. Conditions can change that: if it's windy, or the activity involves less/more moving around, or if it's snowing, etc. The really important thing is to check on your kiddo, particularly their face where there may be some skin exposed, to make sure they're staying warm. It's important to do more than just ask if your kiddo is warm enough; they are more likely to say they're fine (even if they are getting cold) if they are involved in a fun activity they don't want to stop doing.
Also: triple check your kiddo has used the restroom before you suit them up!
What to do outside with kids in winter?
Once you're able to stay warm outside there are lots of activities you can enjoy with your kid in winter! If you have a Burley bike trailer you can add a Burley We! Ski Kit to the mix, which allows you to pull the trailer while you ski, snowshoe, or hike. Or, if you want to turn your kiddo loose on their own you can go with a pair of Madshus Snowpup Cross Country Skis with Bindings. One of the things my kids loved was pretty simple: when we finally got enough snow I used a snow shovel to shovel out a maze in the yard and let the kids play out there. We also found lots of adventure climbing around on the huge mounds of snow left from the snowplows on our street. Sledding is always fun, I made sure we had a pretty big sled that I was able to connect to a harness on my waist to make pulling my kids through the snow a little bit easier. My kids actually really enjoyed going to parks and playgrounds in the winter. Sliding off a slide into fresh snow is super fun!
I also recommend investing in a double wall insulated water bottle. Having warm cocoa on hand has saved many outdoor adventures for me and my kids!
The most important advice is to take it slow and easy and don't hesitate to pull the plug if your kiddo isn't feeling it that day. The most important thing is time outside that they have fun. That might only be 15-20 minutes at the beginning, but all that time adds up over an entire winter season!
Hopefully this helps, don't hesitate to reach out if you have more questions!