I put all four of mine out for naps in the 70s/80s, and they slept soundly for a couple of hours every day. I didn't put them out in fog but they were out in snow and frost.
In winter their clothes, shawls and blankets were wool; I swaddled them when they were tiny. My pram was a big Silver Cross, with high sides and a huge hood, so it was more like sleeping in a little room with the window open. They slept just outside the kitchen window and the moment they woke and moved, the pram would rock and I'd be out to pick them up. I kept the pram in the kitchen when they weren't sleeping so it was always well-aired and warmed through.
In general, babies had more fresh air in days gone by. We had no central heating - we had coal fires and a coal-fired Rayburn - and children were expected to be outdoors to avoid sharing germs.
Oh, and in summer, babies could still sleep outside, as long as there was shade. My pram had a large old-fashioned canopy, so the hood was laid almost flat - the canopy kept the sun off but allowed air to circulate. We lived in a rural village, surrounded by cats and wildlife, but I never heard of a baby being attacked.