Should I cover a skylight well from the inside?
The condensation is typically a sign of either a) too much moisture or b) poorly insulated glass in a cold climate. If the issue is too much moisture, perhaps there's a fix there first (is this a bath, for example?) As for the poor glass insulation, have you considered applying the 3M plastic overlay products in the winter to aid in insulation? 

One perhaps cheaper and easier, albeit uglier, solution would be to cut a piece of EPS or XPS foam insulation board to almost the size of the shaft opening, add some weather-stripping ot the outside edge to make a snug fit, then just push it into the shaft during the winter months. 

I actually have a similar issue in that our house has skylights in the baths with really tall shafts. The ceiling fan is on the ceiling (way below the ceiling light), so during showers, a lot of the hot air rises above the fan and condenses on the window. I've been thinking of covering the bottom shaft in glass as well, keeping the moisture from even getting into the shaft to begin with.