With this recent blizzard we recently saw our ceiling lighting fixture leaking water (slow, about 1 drop every 5 minutes)
I got up in the attic and saw that some snow had been apparently blown into the attic through one of the vents. I removed about 2 handfuls of snow from on top of the insulation, but 2 of the pieces were still damp. Should I remove them? Or will they dry up soon enough? Are there any problems with that?
Also, should I do something to seal up the electrical box from the attic?
If your insulation is damp, chances are good it could freeze or stay damp for a while. If not too much is involved, it would be a good idea to remove it to a warm place to dry out, or simply replace it. Never a good idea to leave wet material against ceiling drywall. It could dampen and ruin the drywall. If left too long, mold or mildew could result. The snow coming through the vents is probably an isolated event. Don't close the vent. Maybe just lay a sheet of 4 mil plastic over the insulation to keep snow off your insulation. Keep an eye on it. If it happens often, consider a better louvered/screened vent fixture that won't allow snow to blow in as easily.
Some types of insulation will not insulate effectively when they are wet. The insulation could grow mould and the water could damage other materials that it comes into contact with such as the the wood fabric of the root, or the ceiling. I would definitely try to dry it out or replace it. Make sure you use appropriate safety equipment (gloves, correctly rated mask) if you touch or move the insulation.
I wonder, if snow is able to be blown in through your vent then can rain also get blown in that way? It might be much more difficult to notice the effects of that as it would be more gradual rather than all melting at once and running though the ceiling, but over a long period the dampness could damage the wood in your loft, the insulation or other materials. I would look into having the vent replaced with one that prevents water getting blown in.