MN in general and the twin cities specifically have loads of great skiing in the winter.  I understand that most ski resorts are going to try opening this year and kids ski free at most until a certain age.  I started my kids at 2 years for alpine, but don't expect to be outside with them for more than 1-2 hours at the most.  They do get bored/cold (even with the right gear because they keep taking it off).  Kids are older now, but this past season, when everything closed early we would still get out into some smaller hills in the state parks.

Keep the energy positive no matter what they are doing, don't expect them to love it right away, but if you make the trip fun they will always ask to come back.  We would frequently stop to climb a big snow pile, build a snow fort in the trees, look at some wildlife, or eat a snack.

Gear wise, toddler's downhill skis with bindings are cheap (~$100) and you can get get some Roces length adjustable ski boots so you don't have to keep buying them new ones each season.  Leave the poles out until they master balance without them.  Also a slope rope is way better than a backpack harness for alpine skiing and they are only about $20.

I personally wouldn't start with cross country skiing until they are over 5, but grab a pair of classic skis, find some flat terrain and pull them on a sled behind you.  That is always fun and quite a workout!

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