That sticky goop is caused by some kind of moisture trickling through your attic insulation and ceiling. It could be rainwater leaking through the shingles, or perhaps coming through some kind of vent. More likely, however, the source of the water is melting frost that forms inside the attic space.

If warm, indoor air is allowed to make its way into your attic, it will cool during winter, condense into liquid water droplets, then freeze on surfaces. This dynamic of condensation and frost build up will continue with frost getting thicker as long as outdoor temperatures are cold enough. When temperatures rise above freezing, the frost will melt and trickle down into the insulation and through the ceiling. The longer the cold spell, the more water dribbles down when it gets warm outside.

Although boosting attic insulation is always a good thing, it’s only a partial solution in your case. There’s enough water involved that you should find the pathway where indoor air is leaking into the attic and seal up the gap. Attic access hatches are the most likely trouble spot. Gaps around ceiling light fixtures are typical culprits, too.

More insulation is a good thing, but I wouldn’t install it until you get the water situation dealt with. An expedition up into the attic is a good place to start. Wait for the next long cold spell and you can probably see where frost is building up.