Why would hydraulic disk-brakes become sluggish in cold winter? Just an incident or due to the cold? Related question, I haven't bled the brakes (again a possible error).

I bought the bike as second-hand and the seller said that the mineral oil cannot be the problem. He said that the mineral oil in the brakes is one-year-old and his dealer instructed to buy a new bike (so I got mine 2-3 years old, driven 10k km). I cannot really trust the words so the rear brakes (no problem with front brakes) may have discolored oil, a thing to watch for according to Shimanos' guide. The caliper is Shimano BR-M485, and apparently other parts are proper (not verified), original Crescent Sport bike brakes apparently (not verified). I haven't yet checked that the brake pads are over 0.5mm as instructed but I feel it is not the problem, speculating. So possible errors:


not bleed the air from the brake system
discolored oil
not tighted some knob(?)
too worn-out pads
weather: perhaps some water in the tank and it freezes or oil vaporizing 
unknown factor (?)


So why would you hydraulic brakes stop working in cold weather? The question is a bit confusing -- the problem started during cold winter and it persists in room temperature. I have earlier repaired inner hubs so is the procedure the same: break thing up to logical pieces and then follow Shimanos insructions or have you found better ways to repair broken hydraulic disk brakes? Again, the term broken is ambigous, the brakes work in a way that you need to press a lot more but now they feel loose (not with the front brake).


Could someone explain what the term bleeding here actually mean?
Must I really use Shimanos' mineral oil and not some cheap substitute?
Which minimum equipments are needed to repair|maintain the-brakes?


Tips to maintain the disk-brakes on low budget welcome.
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.