I have a 77 F150 4x4 lately the brakes are super hard to push like the booster isn't working.... but when the engine gets up to temp the brakes work as usual...it's been cold for here lately single digits at night... could the diaghram that's in the booster just be getting hard due to the coldness.. and then warming up from the heat of the engine?

Thanks to all in advance.

 

There are numerous threads on here describing the in-truck booster test.
maybe do that first to verify.

 

Since brake fluid absorbs moisture, it may be possible you have moisture in the system that's freezing. Probably would'nt hurt to flush the system with fresh fluid even from a maintenance standpoint.