The reason why powder skiing is exhausting is because of something you do in your groomer skiing....
This reminded me of something I learned a long time ago.
I thought I was a pretty good skier when I skied one of my first powder days with a friend who was a top ski instructor. I was struggling, so he told me "Don't turn. Just point them down the hill and plant your pole."
As soon as I planted a pole, I stomped on the opposite ski and buried it (these were old school GS skis), and the other ski floated to the top and crashed me. I had to unlearn the habit of aggressively shifting weight to the outside ski. That worked on groomed trails, but it was a disaster in deep pow.
Before you can learn the skill of independent leg action on powder, you need to lose all the habits that work on groomers but not soft snow, and you need to develop excellent lateral balance skills.
The only two tips that ever helped me in powder were:
The first was "Keep your feet turning all the time." That was from a PSIA examiner, and we were skiing heavy Catskills pow. I think it worked because you need to be balanced in order to keep your feet turning, and because it got me focusing on doing something new instead of going back to habits that only work on groomers.
The other was from a guy who was a mostly intermediate skier, who told me "keep your knees together." That worked because my lateral balance skills weren't developed enough to use my feet independently, and keeping my knees together minimized independent foot action. Also, it distracted me from unfamiliar sensations that I did not have the skill to process adequately. Technically, that's probably not the most effective way to ski, but it doesn't matter because it worked for me at my skill level.
Finally, it's true that any ski will float on powder, even at reasonable or moderately high speed, but wider skis help you learn because they float at lower speeds, and mostly because they react more slowly to weight shifting between the two skis, which is the actual hardest skill in powder.
dm