Icing is not relevant to a PPL. Whilst your instructors comments may be interesting or may have been a “throw away comment” you should not take any comfort from his comments.
Why?
As others have said icing will essentially only occur in cloud or air with sufficient moisture that flying conditions will no longer be visual. Without wishing to be dramatic that is no place for a PPL to be - ever. Should you ever find yourself in those conditions of far far greater concern will be keeping the aircraft level and getting out of the cloud as quickly as possible. Without wishing to be too dramatic, I suspect if you are not clear of cloud before icing becomes an issue it will already be too late for other reasons than the ice!
If on the other hand you are instrument trained the problem with comments such as this is there extreme generalisation. I recall a “little” icing in some wet clouds. On entering the cloud the screen froze over white within 30 seconds, forget watching the wheels or anything else for that matter.
The bottom line is with a PPL never go into cloud freezing or otherwise - ever!