Mine all function just fine no matter how cold. -20 is about as cold as it gets for me though. It's just the battery life I'm referring to. My personal experience is that once it hits -5 any batteries drain 2x as fast and they give off less voltage as well so they hit rock bottom sooner. It doesn't affect your trigger speed, video quality or anything like that. I suppose when the batteries are half dead and it's cold, there might not be enough voltage, so the lights might be dim or flicker. Some of my vids do show flickering on night vids with low battery and cold temps and recover when its warmer. Say I change the batteries late in October, I'll start seeing it in Feb. Keep in mind I do 30s vids and get 300-600 in that time span. I notice issues in the cold more with lithium, but lithium runs like a champ spring to fall.
Its a fact of life with batteries... even lead acid. If you look at buying a portable jump starter for your car, it has a whole graph for temps.
They should sell block heaters for cams that take more than 300 vids LOL
Like you I think cheap cams are the way to go. Expensive cams fail just the same and generally someone buying expensive cams has fewer points of failure before they are out of the game. I've only really had 1 cam fail and I I have running 5-7 cams for several years wintering them. I've had a few eaten by bears though, so dang glad I go with cheap ones.