I started watching in the late 70s but also don't remember goal posts on the goal line. A while ago I wondered about some of the same things you are and so I dug into the history of the goal posts. The history of hash marks also ties into that and the strategic aspects. I'll include the links at the bottom if people want to read more, but I'll post a few main points here for people who don't have the time.
A couple of things that I learned - the NFL originally used the NCAA rulebook and had goalposts where they are today. The NFL later created its own rule and moved them to the goal line in the 1930s - likely to encourage more FG attempts and lessen the chance for scoreless ties. In 1974, the NFL moved them to the back of the end zone for the opposite reason -- to discourage longer field goals and encourage more touchdowns. In the older photos, you'll see the goalposts exactly on the goal line (I don't know what year this photo was taken):
https://www.stadiumsofprofootball.com/s ... e-stadium/ -- at some point they moved them back a bit, someone else might remember when that happened and why. Here's a photo from then City Stadium in 1957 when the goalposts were offset from the goal line:
https://www.packers.com/news/yes-lambea ... ed-in-1965
The NFL moved the hash marks closer together -- aligned with the goalposts -- around the same time they moved the goalposts to the back of the end zone. Kickers like Ray Wersching and Chris Bahr learned they could line up their kicks with the hash marks rather than look all the way to the goalposts. That is likely one reason why kickers are so much more accurate today -- the goalposts line up with the hash marks so they can aim in between the hash marks, also they're not kicking at extreme angles near the goal line like they once did. As far as I know, the ball was always placed on one of the hash marks, except maybe for extra points -- somebody else might no the answer to that one? The saying that the old-timers used to use on defense was "Old man sideline never misses a tackle" -- the wider hash marks helped the defense somewhat in that it shortened the field on one side for the offense. The further you go back, the further apart NFL hash marks are. You might also notice that the hash marks are still further apart in college football than they are in the NFL.
As for the Ice Bowl, I've gotten to speak with a few of the Cowboys defensive players about it, and nobody ever mentioned anything about the goalposts that I can remember. They spoke mostly about digging into the frozen turf during the time out before the sneak to gain some footing.
The goalposts on the goal line did affect the outcome of the 1945 NFL Championship -- Sammy Baugh threw a pass from his own end zone and it hit the goal posts -- that counted as a safety at the time. The (then Cleveland) Rams beat Washington by one point - 15-14 to win the championship.
https://www.thegamebeforethemoney.com/goalposts/
https://www.thegamebeforethemoney.com/a ... ash-marks/
Embarrassing question, but I know this is the place to ask.
