freeski919 in post #3 has great advice. So do others. Let me add a few comments.
--skis----you need skis with the flex distribution that works well in deep snow. That's what powder skis do. Before we had fat skis, we had powder skis that flexed evenly in the tip & tail. Rent powder skis on a deep snow day.
--snow quality---deep wet snow is really difficult. Stay on the groomers. Deep dry fluffy snow is a gift. Oh, it's nice!
Look at this pic:
The way he's curving his body to put his skis on edge is called angulation. (The way he's twisted his body toward the outside of the turn is called counter, also important. I'd like to see his inside hand higher, though.) So, looking at the bases of his skis--if the snow was deep, with the skis at that angle the snow forms a platform under the skis, curves the skis, and the skis turn you. You do not turn your skis. Try this (or imagine you try it)...put a ski down on a soft surface like a row of pillows and push down hard on the binding. The ski curves. That's what the snow does to the ski. That's how the ski, on edge, turns you. Visualize an airplane in the sky banking in a turn. Visualize your skis down in the snow banking a turn in the snow. Works the same way.
Here's what you do. Keep your feet close together. Equal weight on both feet. Stand almost straight. Standing still, practice angulation. Skis across the hill aimed to your right just like the photo, have your partner pull forward on the fabric of your right shoulder while he pokes a finger into your ribs on the left side. Bend in your trunk, not at the waist. Compress the ribs on your left and stretch your back on your right. Get your head & shoulders out over your skis, way out, while your hips are rounded back for balance. This isn't sticking your butt out, this is an easy rounded movement like you see in the picture above. Look at your skis and see how they're up on edge. This how you move to make a turn to the right. Again, you don't turn your skis. You put them on edge and they turn you.
To release (end the turn), easy, just relax both legs. Your skis flatten themselves and float up. You don't need to see your skis, they don't need to come up to the surface, but it's OK if they do. angulate & counter the other way, tilt those skis so they bank in the snow, and you'll turn the other way. Stay fairly tall, but angulate & counter as much as you need to produce the turn radius you like.
Somebody above said don't sit back. Exactly right. Do this--on a straight easy bit in deep snow, ski along at moderate speed, across the hill if needed. Push your feet slightly forward. Pull them slightly back. Feel the difference in how your skis respond. Find the position of your feet under you where your skis are easily responsive, not diving and not coming too high to the surface, 'cuz you're sitting back. That's your center point for this pair of skis (other skis may like a slightly different position). Remember this position with this feeling of your shin against the tongue. Always return to this center position.
When do we want to sit back? Two conditions. 1--when we're about to ski up on a rise, so we temporarily lighten the tips by pushing our feet forward, then we immediately re-center after we're up on that rise. 2--when the snow is so wet and sticky that we won't reach the bottom of the hill unless we keep the tips up. We sit back, strain our quads, and finally reach the bottom of the hill in this slop. Ugh.
The angulation and counter are important on packed snow as well, except you have your weight mainly on the outside ski. In both types of snow, roll your inside ankle so the big toe of your inside foot is tipped up in the air. That's an important first step for getting your skis up on edge. Don't roll the outside ski up on edge--your body position will do that. Don't drop a hip toward the snow nor drive a knee toward the snow. All the effort is in that ankle, and everything else is allowed to move to make the smooth easy movement.