The certified flight instructor (CFI) of the Piper PA 28-161 stated that he, a student pilot, and a passenger were conducting an instructional flight in actual instrument meteorological conditions. They returned to their home airport on a cross-country flight, and the CFI executed an instrument approach uneventfully. The airplane then landed on runway 16, a 5,001-foot long, 100-foot wide, asphalt runway. About 5 seconds after touch down, while traveling about 50 knots, the CFI observed four or five deer on the right side of the runway. While the other deer scattered away from the runway, one deer ran onto the runway and into the airplane. The CFI swerved the airplane in an attempt to avoid the impact, but was unable. During the impact, the right wing sustained substantial damage. The reported weather at the airport, about 30 minutes after the accident, included wind from 140 degrees at 5 knots, overcast ceiling at 300 feet, and visibility 7 miles.