Fishing wire through exterior wall -- what problems am I likely to encounter?
You may or may not have fire blocks, depending on the height of your walls (a quick search suggests 10' or higher) and the codes in place at the time your house was built.  However, in a 1986 house, you'll  definitely have drywall so a decent stud finder would be able to tell you quickly if you have them.  Run it horizontally to find the studs, then vertically where you want your wiring to go to see if it picks up anything in the cavity.

If you do have a fire block, you can get flexible drill bit extenders so you can drill a hole through it.  Probably easiest to do from below (where you're cutting the opening for the electrical box) unless you have a gable at that point on the wall.

Apart from insulation, other issues you might run into include:


other wiring near the spot that you're trying to use;
covered-over windows from earlier remodels;
sheathing nails missing the studs they're supposed to be going into;
if you have loose-fill insulation, it'll all come pouring out when you cut a hole for the electrical box.