What I remember most about The Cold War era is things like Air Raid Shelter signs on buildings and having to do the "duck and cover" drills once a month while in elementary school (mid to late 1960s). People were terrified that nuclear war could break out at any time, and we'd all be wiped out. Those were scary times, for sure.
As far as aviation goes, I grew up four miles northwest of New Castle County Airport (KILG) in northern Delaware. It's a Tactical Airlift Command base and home of the DE Air Guard, currently a C-130 unit. Back in the 1960s, however, there were C-97s and C-121s in and out of there all the time, with those thundering radials churning out sweet sounds as they climbed out from the airport, often right over our house (especially if they took off on Runway 31). There were also plenty of piston-powered civil freighters operating there. The Thunderbirds were flying Phantoms, and the Blue Angels were flying Phantoms and then Scooters. The space program was going full speed ahead, and I was really into it! We were bombarded by TV news reports from the Viet Nam war, and there was lots of film showing warplanes in action. We didn't have a color TV, so I got to see it all in glorious black & white.
Not sure why I remember this so clearly, but one day while I was outside on recess in the school playground, I heard faint turboprop engines overhead and looked up to see an Armstrong-Whitworth Argosy flying over! Only one I've ever seen, to this day. That must've been about 1967.
Around 1971 or '72, we were visiting my grandparents at their rural home on a mountainside in the Ozark mountains in Missouri. Two fully-loaded USAF Phantoms went screaming over the house at probably 100 feet, super-sonic, down the valley and up the side of the opposite mountain! The sonic boom broke every window in the house and garage and scare the living daylights out of all of us! Of course, my grandfather was on the telephone almost instantly, trying to find out how to contact the Air Force (which he did, and they paid for the windows). Luckily the windows of his pickup and my dad's station wagon didn't break. I assume the Rhinos were practicing some kind of tactical low-level target approaches at combat weight. All of the grownups were furious, my little sister was bawling her eyes out, and I thought it was the coolest thing I'd ever seen!
Occasionally, I'd hear jet noise and look up to see a B-52, or several, cruising overhead at high altitude, and each time I saw them, I wondered if they were heading for the USSR, and life as we knew it would be ending in an hour or so. Yeah, those were scary times.