I would agree that the depth of the lake/pond in which you are skiing at DOES NOT affect how you ski. Skiing is a sport that really only requires 4-6 feet of water. Colder temperatures make the water more viscous therefore the water is more dense due to the condensed molecular structure on the surface of the water. (The molecules aren't moving as fast). More density means for buoyancy to an extent, if you're more buoyant you're not "plowing" through the water (less drag) you're not sinking as deep. The viscosity of the water doesn't actually change until a decent depth. Long story short, your ski will ride higher on "thicker" water than it will thinner water.
A factor could also be the ski itself. Carbon and or fiberglass may react differently to different temperatures. The width of the ski. @Horton makes a good point about air density. To my understanding the air pressure theoretically should make the water denser If it has nowhere to escape to if that makes sense. Unfortunately I believe the idea is a bust because water is an impressible liquid. Put water in a pan and fill it to the brim, press down on the water with your hand. Spoiler alert, it overflows.
However I'm gonna disprove my own theory (great idea right)