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
Hmm....not strictly correct. I used to hold a PPL and IR and would regularly fly in cloud. It is worth considering that when the MEA is up to 11,000', you may get icing even in sunny climes like California....
But I know what you're saying