I have my doubts about this theory. Here's why:
The bees that are in the hive right now, were born in October. From their perspective, days right now are about 30% shorter than when they were born. But: that is almost exactly the same for bees born in July (days are about 30% shorter in October than in July). If the length of day is a marker of winter for the bees, why don't the July bees think it's winter in October?
As for the height of the sun, we'd have to know whether bees measure it from the horizon or from straight above, but if we assume they measure it from the horizon, then: the angle of the sun is halved between October and now... but the angle is also halved between July and October.
I think it far more likely that bees know it is winter simply because of the temperatures.