cold weather/ brakes

Completely normal. The colder it gets you will hear creaks and groans and parts like brakes and suspension will be stiffer because of the temperatures, the various fluids and lubes get stiff and even the parts like rubber and plastics will get stiff. I just wish I thought of 50 as cold, it's currently -4 here and it isn't the cold part of winter yet.

It’s just unnerving when I go to start my car and push the brake and it’s rock hard and I thought it was a vacuum issue but it seems to depress once the cars started it’s just unusual because it was cold last week and didn’t do it

Totally normal though. As soon as you started it the engine created vacuum and helped pull the pedal. If the engine isn't running there is only residual vacuum in the system and depending on what the vehicle uses it for and what is on when you shut the engine off determines what is left. You got in and most was gone, so no pedal assist. Next time it might have full assist. Just the way the system operates. The reason you need to step on the brakes to start the engine is because of multiple times that people started their cars "in gear" even though neutral switches have been installed since the 1930's. So they mandated that you have to step on the brake to start the engine and in many cases you have to step on it to shift as well.

It's super stiff sometimes while other it's semi stiff with less resistance that's why I was confused because I drive my car everyday and haven't had that happen in quite some time until this week when I noticed a dramatic temp decrease so I was wondering if it was that or just fluctuations in pressure itself

Totally normal on vehicles. It's why they start the engines on vehicles in the artic and leave them running for weeks, Keeps the fluids warm and circulating. Cold weather is a pain most times because it makes vehicle stiff and if you are out in it your body starts to get stiff. Nothing to be concerned about, just life with a vehicle.