Why would hydraulic disk-brakes become sluggish in cold winter? Just an incident or due to the cold?
Hydraulics are the same for car brakes, as for these style brakes, as anywhere else in the physical universe. 

Liquids have an amusing property that they do not compress well, if at all.  (They do of course compress, but not very much in the grand scheme of things, and it takes a lot of pressure to noticeably compress them).

Thus your hand started breaking force is transmitted direct to the brake, through the medium of the fluid.

If the fluid is getting viscous, due to cold weather, it might become thicker, and thus less responsive to your hand pressure.  

The reason to bleed air out of the system is that air compresses very nicely, thank you, unlike a liquid, and so destroys the hydraulic principle in use.   Bleeding in this context means to release any trapped air inside the hydraulic cylinder.

Same as in car brakes.  First the air compresses, absorbing much of the energy being applied to brake, until finally the liquid starts to transmit the energy.