I was skiing the trees at Steamboat on a powder day with a bunch of people.  I was standing on the uphill side of 2 aspen trees that were about 3 feet apart or so.  I waited until everyone had gone because I wanted to ski last.  I was just about to go when my down hill ski sunk and I tipped over down hill.  It was just one of the stupid things that happens, but now I was laying on my side with my head going downhill and my skis were above the 2 aspens.  I had my dins set at just about the max and I was completely fucked.  The snow was deep.  I couldn't roll out of it, because of the trees.  I tried releasing my bindings with my pole, but I had to do it all with my arms.  It wasn't working and I thought it was all over for me.  I was starting to panic.  Finally I just laid there for awhile and caught my breath and then used every ounce of strength I had.  It worked and I got one ski off.  That was enough for me to get out.  I couldn't believe how tired I was from just that.
If you are going to be skiing in deep pow, I would suggest laying down with your feet uphill from you and see if you can still get your skis off.  If you can't do it, you might want to lower your din settings until you can do it.