most of Ohio is
zone 5 or 6, and since its
growing along your house, I'll take it that it's perennial. I'm going to assume that you have English Ivy (Hedera helix). English ivy is tough, and you should be able to cut the dead portions off - regular pruning and cutting back will actually help keep it vigrous and under control. Cutting
growing vines will make the vine branch out as it grows again.
To keep it under control when it climbs on trees, it's suggested that you cut all the vines at a reachable height. The rooted portions will survive and send out multiple shoots, and everything above the cut without roots will die. You can do it to 'revitalize' your ivy to make a new green flush of foliage, but until it leaves out, you'll be stuck with a slow dying mat of vines.