Before you make plans to hike into a pond or lake that has trout, make sure you confirm that ice fishing is allowed on that water. Most waters having trout are closed to ice fishing, and if they are open to ice fishing then live bait may be prohibited. The DEC annual fishing regulations book that is available any place that sells fishing licenses lists all of the waters in the " special regulations by region " where ice fishing is allowed.
I think the basic regulation is that if the water has trout then it is not open to ice fishing before April 1 unless it is listed in the " special regulations by region " sections as being open to ice fishing.