I think you did a great job with your knowledge and experience. Personally, I think you knowledge was lacking for the task you were attempting (lack of experience is a given), but you overcame it with some good decision making. Your aircraft is not equipped to fly in icing, you have no equipment to battle it.

Open the Limitations chapter in your POH. In there, you should find the words:

"Flight Into Known Icing Conditions Is Prohibited"

Flip to the Emergency Procedures Chapter. In there, you should find a checklist for:

"Inadvertent Icing Encounter"

Either you had forgotten either of these items, or you were not aware of them because you had not read them before.

Your study materials should have a section on weather, there should be a part in it about icing conditions. Here you can learn what aircraft icing is, why it's hazardous, and how to predict or detect it. And what to do as soon as you recognize it. You made a good decision to descend, but you waited way too long before you made that choice. That's okay. You didn't know what you were getting into.

Have fun with the training, study hard, and stay safe. Mother nature took the opportunity to teach you a lesson, and you weren't prepared, but you managed to land in once piece.

Hope this helps,