The 4WD lamp is grounded by a trigger switch/plug located on the passenger's side of the reduction housing of your transfer case. For your 1986 truck, this is a single wire switch that simply sends a ground signal to the lamp which is powered (whenever the key is in the ON position).
If its related to the weather, than its possible the rubber coating seal of the switch is damaged, and water was able to get inside the switch and short it out (constant ground), or water got inside and slowly rusted its internals and it just needed 1 more cold night before it gave up the ghost.
Otherwise, because it's a simple ground, it's possible it's wire has been shorted somewhere between the switch and the lamp (another way to have a constant ground). Maybe a rock hit it, or it was slowly rubbing against something.
The easiest way to check if it is a faulty switch or a short in the wire somewhere is to simply unplug the switch at the transfer case and check if the lamp turns off (in 2WD & the key in the ON position). If so, then you have a bad switch. If not then you have a short somewhere in the wire leading to the lamp.
The 4WD Lamp Indicator switch / plug in question is this one:
Good luck
BigMike
