"They lived in a forlorn-looking house that stood alone and had an air of starvation. A few straggling savin-trees, emblems of sterility, grew near it; no smoke ever curled from its chimney; no traveller stopped at its door. A miserable horse, whose ribs were as articulate as the bars of a gridiron, stalked about a field, where a thin carpet of moss, scarcely covering the ragged beds of pudding-stone, tantalized and balked his hunger; and sometimes he would lean his head over the fence, look piteously at the passer-by, and seem to petition deliverance from this land of famine."
Irving describes the house as neglected and starved. The strict "economy" of the pilgrim fore fathers had be taken to the extreme of being miserly and cheap. The Walkers even are cheap and selfish with each other, constantly looking to hoard any advantage or wealth they accumulated.
See the them concerning Greed