My first car that was fitted with ABS had an operating threshhold of 14 mph+.

Just at the outset of the recent snows (whilst working in Fife) my current car's ABS packed up, owing to a failed sensor. I left fixing it until this week, I found driving in snow without ABS much more comfortable, they seem to cut in at much lower speeds now.

Yes, basically. If you lose grip, ABS effectively disengage the brakes until it can sense no further locking of the wheels. But only so long as you a still travelling forwards in a straight line. Once you have gone sideways, it is too late even for much cleverer systems such as stability control. When you are on the cusp of going sideways, stability control may well help lot, but again it really depends on the level of grip available.

When deceding a snowy or icy hill the general advice is to use engine braking and not the brakes especially as a light rear end will very quickly lose grip as you have found out.

Again, cold weather tyres help a lot. They are said to have about three times more grip than 'summer' tyres on both snow and ice.