Preston shaded the possession in what was an even game for long spells, and a point apiece means that neither team has moved in the Championship table, with the hosts remaining in 13th position.
A floodlight failure meant that kickoff was delayed by five minutes, and it took both teams a while to settle into the contest.
Bolton's Josh Vela tested Preston goalkeeper Chris Maxwell with a long-range strike in the 31st minute, but that was just about the closest that either side came to making the breakthrough in the first half of action.
Henry came closer in the 74th minute when his thunderous effort looked to be testing Maxwell, but the ball narrowly missed the Preston goal, and an uneventful final 15 minutes failed to produce an opportunity of note.
Bolton have now not lost in their last six Championship matches - four of which have been draws - while Preston are without a win since beating Hull City towards the end of September.