I ask this question from the context of formation-flying, such as during WW2. What is the visibility in a typical cloud during daytime? Can you lose your wingman right away? Were you at serious risk of mid-air collision when this happened?
The answer is that visibility varies depending on the density of the cloud. And it can vary significantly.
Flying in formation in IMC is very common in the military. Sometimes it will be dense enough that all you will have is a wingtip or light. In those cases it can be very disorienting and difficult to maintain position because you need more than a single point to discern relative motion. The stress level can go up too since the denser the cloud the closer want you fly to keep sight. But generally those sort of conditions are relatively brief, and within 10-15 seconds you will likely have the wing and fuselage back in sight.
For reference, in close formation the wing tip might be 10-20 feet from your canopy, with the lead's fuselage another 20 feet beyond that. So, the worst visibility I have seen (when I lost sight) could have been anywhere from 0-20 feet. If you see the lead clearly the visibility could be anywhere 50 feet to a mile or more. You just don't know, all you see is another airplane and gray... There is certainly no absolute or standard number.
Every formation flight brief should cover lost sight procedures in case it becomes dense enough to require a break away. I have only ever lost sight and had to break away once.