If the trees were on your neighbor's property and the neighbor knew or should have known that the trees posed a foreseeable danger, then you may have a right to recover against the neighbors personally or via its homeowner's policy. You may wish to consult an arborist regarding whether the trees were foreseeably dangerous before the ice storm or whether the trees fell by an act of God.
In the first instance, if you had howeowners insurance coverage as of the date of the incident, that insurance should provide coverage for the loss. If you did not have such coverage, then you could bring suit against the neighbor. The critical question in such a case would be whether your neighbor should have known that the trees posed a risk of damage to your house. This would be determined, among other things, by their size, distance from your house, configuration, etc. A case like this is typically handled on a contingency fee; in other words, the attorney does not earn a fee unless he/she secures a recovery on your behalf.