Do you really put an ice pack into a bag or wrapped around a towel before applying to injured areas?

A thin towel is best. Ice should never be placed directly on the skin to prevent "ice burns" to the skin. Best to wrap the ice bag in a thin towel to keep the ice directly off the skin.
Avoid frost bite. The ice directly on your skin can cause frost bite, just like getting out in the cold in alaska in january. The thin towel helps to prevent this by providing a barrier between you and the ice while still letting it do its job.