I think they saw nature in a spiritual way as the collective "Over-soul" of all the souls that create and reside in every form in creation. That means that very soul is one with and is the Over-soul, which some call God, but Dickinson and Whitman may have thought that word had to much connections to organized religion which has a different definition than they had.
For Dickinson, the character of nature helps us to understand the universality of human experience and for Whitman, the nature is the human identity represented by barriers such as water or land which are created by the writer.
In both poets, we can hear the voices of nature in many corners of their letters.
