There are two common under-hood causes for tough start/poor running for a short time in damp weather.

One is the high-tension wiring which runs from the coil to the distributor, and from the distributor to each spark plug. The insulation degrades over time and develops very small cracks; moisture and dirt fill the cracks. When damp, the HT current finds its way through these now-conductive cracks to ground, and the current doesn't reliably get to the spark plugs.

The second is the distributor cap. Made of a plastic material (bakelite?), it too develops cracks with age. Again, HT current can leak to ground in damp weather.

In the dark, have someone else crank the motor while you look into the engine compartment. You can often see sparks. When the engine warms, the dampness is reduced by engine heat, and the current doesn't leak to ground so readily.

Replacing the HT wires and distributor cap solves this problem.
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David Brick, Santa Cruz CA, 1988 245