If a power-brake booster doesn't work, then you have a vacuum problem.
I have an 1982 Honda with 144,000 miles. One fall morning I started to go to work and the brake pedal was as hard as a brick. The brakes still worked if I stood on the pedal, then after a couple of minutes, the pedal was normal. I had Honda check the problem, they said "Brakes OK." The next day, it was worse (it took longer to get back to normal). So I took it to a trusted garage and they said, "Leave it overnight so we can verify it, but it looks like you need a new power brake booster."
The next day they experienced the problem and replaced the power brake booster. The following morning, it did it again, so back to the garage I went. They kind of mumbled about vacuum problems, but called and said they had replaced the new brake booster with another new brake booster, kept it another night, said it was OK, and off I went. This morning I had the same problem, but it did clear up more quickly. Do I widen the brake pedal so I can put two feet on it and grunt, or can you help me? -- Gary
RAY: Oooh! They were so close when they were mumbling about "vacuum problems," Gary.
TOM: The power brake booster is vacuum-operated. And it sounds to me like it's not getting enough vacuum when you start the car.
RAY: I'd start by checking the vacuum reading right at the booster. Leave the car with your mechanic overnight again, and have him connect his vacuum gauge right between the booster and that hose that runs to it. The next morning, he can have an assistant start the car and confirm that the brakes are hard, and then he can read the vacuum.
TOM: Under those cold-start conditions, the booster should be getting maximum vacuum (which should be close to 20 inches of mercury). If you're getting much less than that, you have a vacuum problem.
RAY: You can check to see if you have a collapsed hose running from the intake manifold to the booster. But I don't know why it would "un-collapse" after a few minutes. You'll have to write to the "Dear Albert Einstein" column if you want an answer to that (is he still writing that?).
TOM: It's more likely that after 144,000 miles, your engine is simply wearing out. You may have lousy compression (and therefore lousy vacuum) when the engine is cold.
RAY: Why only when it's cold? As the engine warms up, the pistons and rings expand and form a better seal. That increases the compression and the vacuum. And that would explain why this is a cold engine/cold weather phenomenon.
TOM: But if compression is the problem, it's going to slowly get worse. And the solution for bad compression? An engine rebuild, or a new car loan. Good luck, Gary.