On Earth over the course of time, a permanent cloud envelops the planet due to various reasons. However, unlike a nuclear winter or permanent ash cloud situation that completely blots out the sun, this cloud is opaque to a degree. Sometimes there's space/gaps in-between the clouds like a normal day, so sunlight can shine through them and once could see the sun. Other times the cloud is more solid/thick like. Essentially a cloudy or rainy day but with a little more sunlight and brightness than we see normally here on Earth.
At any given point on Earth, there is never a spot that is cloud free or fully exposed to open air.
Would such an opaque cloud coverage cause a nuclear winter/ice age effect where the temperature of the planet drops drastically?
Drastically in this sense means that the temperature falls so much that the effects are catastrophic for the environment. Slightly colder weather wouldn't be considered drastic. One can assume that there are still things like rain and snow fall like normal.