Personally I don’t think techniques get in the way of each other, so this wouldn’t be a bugbear of mine. I would rather follow the kids’ enthusiasm, because enthusiasm saves a lot of whining! However, when focusing on any new skill, it’s smart to break things down.
Skiing is about core strength and balance, so keep the sticks/poles away, maybe for as much as a couple of seasons. This is the tried and tested advice for setting out with Nordic skiing as well as downhill skiing. The legs and the core of your body are learning to control your movement on skis, the sticks are an added tool later on for building momentum in Nordic skiing and for speed of turning in slalom. Both sports could be done without sticks if you wanted to.
Ski boots are weird! Heavy and counterintuitive for the child! This is not the time for hand-me downs – make sure socks provide optimal insulation and that the boots are a perfect fit – this limits how much blood flow is restricted. Downhill skiing is an unusual combination of an all-body workout and sitting perfectly still in chairlifts which are extremely exposed to the elements – warm feet are massively important but quality base layers all-round make all the difference.
And prepare at home. Dry ski slopes are a thing with the Brits but my preference is to take my children ice-skating. Skating is a fun activity in its own right, and the skills transfer beautifully to skiing. There are plenty more ice rinks in this country than dry ski slopes so make it easy for yourself.
Finally, don’t overcommit. Some 3 and 4 year olds can’t wait to hit the slopes, but skiing doesn’t have the instinctive playground appeal of ball games or running races. Break it up. Bring hot chocolate. Throw snow balls. Muck about.