Ignorance was bliss

Down in Rochester, we've had quite a few pretty strong storms come through this summer. We have a huge (about 48" diameter at breast height (DBH)) silver maple next to our house, and need to get a couple of low branches off so they don't crush our house (or the neighbor's), but we want to wait till winter so it'll cost about $800 instead of $1500+. The tree's healthy, so likely if we got a storm strong enough to tear off its branches, we'd have other problems too, but now every time a strong storm comes through I get paranoid. My main concern is that since it's a fast-growing tree, the wood is softer and a bit weaker than, say, a typical oak of comparable size. Realistically, the tree's been there for years, and nothing's happened yet - it should be find for another 4 months, right?