How did you not get completely stuck in the mud in between snow patches?
Brownski's advice is good and he is now a pro. My unsolicited amateur thoughts: Be safe, have fun, think about the terrain and have fun.
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If thinking about it from a principle perspective, you can categorize that you have to adjust to how that particular condition will ski (or affect the combination of your mass in its position over skis in motion).
1. Mud and grass is going to be much, much slower, so you will have to adjust to it pushing your upper body forward (so leaning back sounds like a great tactic - think about when you are on a train or in a car and you come to a stop - your body still wants to go forward. Physics I say : ) ). If it is a small enough patch, another way to avoid the issue is ski around or over - small jump from snow to snow over mud. Again, the jump is one I would ABSOLUTELY practice on easier terrain first.
2. In addition to thinking, you can find easier terrain and apply trial and error in a controlled and careful manner. I am talking the easiest terrain you can find, like any other new skill. I am pretty sure I am on the bunny slope every season and I am a strong skier.
3. And I am always a fan of getting a lesson with a pro. Whether it is my wife or my kids I ask for a cert III, cert II min. Plenty of uncertified or I are great, but at least you know these folks had to jump through a bunch of hoops (which can be good and bad but the bad isn't that bad). Sometimes you will get a III that doesn't ski the most challenging stuff anymore, but sounds like you may not be initially focused on that.