Perhaps bringing the choice of driving the car in winter on summer tires or in summer on winter tires is exaggeration but I enjoy my:
- snuggy, stiff sole, grabby heel, and super light road shoes on light, stiff and streamlined road pedals with no possibility of unclipping accidentally on my road bike
and
- sturdier, a bit warmer, snuggy but with some wiggle room, with stiff and grippy sole, light by MTB standard, MTB shoe on a light but durable MTB pedal that will not get clogged with mud and stones and will allow me for slight floating and easy in and out while on my CX bike.

But these are just MY personal preferences if not requirements. One can mix and match any of these to her/his likings.
There probably are more attributes one can consider but I am just trying to make a point that while it is possible to ski powder on carvers or ski the groomers on your 130mm fat skis there is a purpose for the specific kind of gear and specific conditions. Not to say that everyone has to comply. After all, it's all about enjoying the time on the bike.
Cheers