Soak wood chips for 1 hour prior to smoking.
Prepare a smoker to a constant 225 to 250 degrees F. Drain wood chips, and place half over the lit charcoal.
Place the beef tenderloin in the smoker. After 30 minutes, add remaining wood chips to the charcoal. Continue cooking until desired doneness is reach (In a 200 degree smoker, it will take approximately one hour to reach medium).
Serve warm, cold, or at room temperature with tarragon sauce and horseradish mustard.