if the bead has come off the rim, check the bead and see if there is corrosion on it, that is a common one that we see.
with the way the weather is going, we see alot of mystery leaks that usually turn out to be snow getting into the valve, melts, people check pressures and it gets stuck in the valve and when it gets cold again it will freeze, expand and cause the valve to leak again and will usually continue for a while.
I would say stay away from any tire sealants as they are usually toxic, can peel coatings off wheels, damage tires, and cause the tire to become out of balance if not used properly, I am guessing you do not have tpms sensors, but if you did, it would also mess them up and they are not a cheap fix.
if you can get the tire in a warm garage, spray it with dish soap and see what you find(when the wheel is nice and warm as the cold will let the water freeze and may not bubble. if nothing is found, make sure the stem is snug and dry(even let a little air out to clear it) and hopefully you will be ok.
good luck
steve