Those depressions could be a depression in the bedrock which hold water like a basin, there is nothing much you can do about that, they even maybe a spring head.We have a boggy area at the bottom of the hill, it is just a flood plain area and you cant drain a flood plain as that is the lowest point. Willows thrive in wet land but dont dry it up. We wanted to plant hundreds of trees along our burn but they said no as it was an important habitat in its own right and I could claim a grant for doing nothing! If you have a peat soil you must look after your grass, grazing grass is not natural for peat and will just slime away on the wet, acid soil in winter and the weeds will grow especially dock and ragwort. Weeds grow faster than grass!