For portraits, I think an overcast day can be great. Especially when the you can see the disc of the sun. It creates a very luminous and flattering light. Kinda like God's giant softbox. When the clouds start to get too heavy and grey, and the sun is really obscure, then I tend to stop shooting. Although, playing around with fast films and grain can sometimes be very effective when it's really grey out.
That said, I shoot far less film in the dead of winter, when the days are greyer, and spend far more time in the darkroom printing up summertime photographs.